Inside a conductor E=0 everywhere, = 0 and any free charges must be on the surfaces. "name": "Q.3. Because gravitational potential decreases inversely with distance to source mass, whereas gravitational acceleration decreases inversely with the square of the distance, the geoid provides a long-range probe into Earth. Total work done (W) by the external force is determined by integrating the above equation both side, from r = to r = r, The potential at P due to the charge Q can be expressed as. "text": "Ans: No, there can not be a non-zero component of the electric field along an equipotential surface." As the name suggests equipotential surfaces are the surfaces such that every point on the surface has the same potential. If you're seeing this message, it means we're having trouble loading external resources on our website. },{ The equilibrium, energy-minimizing and surface-area-minimizing shape of a liquid droplet held together by surface tension in a universe operating under the infinity norm must be a cube--and more specifically, an axis-aligned cube. A surface on which at each and every point potential is the same is called an equipotential surface. We can identify strong or weak fields by the spacing in between the regions of 1equipotential surfaces, i.e. The equipotential surface is directed from high potential to low potential. The Great Soviet Encyclopedia, 3rd Edition (1970-1979). The equipotential lines can be drawn by making them perpendicular to the electric field lines, if those are known Note that the potential is greatest (most positive) near the positive charge and least (most negative) near the negative charge. The points present in an electric field having similar electric potential are called equipotential points.. Note that in the above equation, E and F symbolize the magnitudes of the electric field strength and force, respectively. Jahnavi said: "Equation of a surface" and "expression for potential" are two different things . The particle moves on an equipotential plane of \(V = 1\,{\rm{V}}\)after \(t = 0.0002{\rm{s}}\). so the voltage will stay the same on the surface and on the equipotential line because it takes work to make a change in voltage, and since no An equipotential surface is a surface that has the same value of potential throughout. ", An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'. For a uniform electric field, the equipotential surfaces are planes normal to the x-axis. Equipotential surface is that surface at every point of which electric potential is same. The electric intensity E is always perpendicular to the equipotential surfaces. b. perpendicular to the electric field at every point. A charged particle having a charge \(q = 1.4\,{\rm{mC}}\) moves a distance of \(1.4\,{\rm{m}}\)along an equipotential surface of \(10\,{\rm{V}}\). A Parallel Plate Capacitor With Square Plates Is F. As shown in the figure, chargesare placed at the vertices. In simpler words, any surface that has the same electric potential at every point is known as an equipotential surface. EQUIPOTENTIAL SURFACE It is a self defined term, equipotential surface - means, surface which having the same electrostatic potential. See the answer Show transcribed image text Videos Step-by-step answer 02:01 100% (6 ratings) Expert Answer For stronger fields, equipotential surfaces are closer to each other! A solid conducting sphere, having a chargeQ, is surrounded by an uncharged conducting hollow .. As a result of the EUs General Data Protection Regulation (GDPR). The explanation given to the answer of above question, was "Electric field is always perpendicular to equipotential surfaces". An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. School Camosun College; Course Title PHYS 104; Type. A surface having the same potential at every point is referred to as an equipotential surface.There is no work done in order to move a charge from point A to B on equipotential surfaces. B) Work is required to move the negative charge from point A to point B. An equipotential surface must be A. tangent to the electric field at every point. In other words, any surface with the same electric potential at every point is termed as an equipotential surface. If there is an . E= dV/dr E 1/dr. "@type": "Answer", Question: An equipotential surface must be. Why is the electric field always at right angles to the equipotential . (2) that the (infinitesimally close) points "1" and "2" are on the same equipotential surface (i.e., V 2 = V 1) if and only if =90. Equipotential surfaces allow an alternative visual image in addition to the image of electric field lines around a charge arrangement. Somewhere between these negative equipotentials and the positive ones produced by the accelerating voltage is a zero equipotential surface that terminates at the filament. A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. The negative sign represents r < 0, W is positive . If points A and B lies on an Equipotential surface then V (at B)=V (at A) W= V (at B)-V (at A) W=0 acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Fundamentals of Java Collection Framework, Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Data Communication - Definition, Components, Types, Channels, Difference between write() and writelines() function in Python, Graphical Solution of Linear Programming Problems, Shortest Distance Between Two Lines in 3D Space | Class 12 Maths, Querying Data from a Database using fetchone() and fetchall(), Class 12 NCERT Solutions - Mathematics Part I - Chapter 2 Inverse Trigonometric Functions - Exercise 2.1, Torque on an Electric Dipole in Uniform Electric Field, Properties of Matrix Addition and Scalar Multiplication | Class 12 Maths. . "text": "Ans: An equipotential surface is a surface that has the same value of potential throughout." It is impossible for two equipotential surfaces to intersect. An equipotential surface is one that has the same potential value throughout. Literature. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be, A constant power is supplied to a rotating disc. Goyal, Mere Sapno ka Bharat CBSE Expression Series takes on India and Dreams, CBSE Academic Calendar 2021-22: Check Details Here. If a curve or a line connects these points, it is referred to as an equipotential line, and when these points lie on a specific surface, such a surface is called an equipotential surface. Since any surface having the same electric potential at every point is called an equipotential surface. Equipotential surfaces associated with an electric field which is increasing in magnitude along the x-direction area)planes parallel to yz-planeb)planes parallel to xy-planec)planes parallel to xz -planed)coaxial cylinders of increasing radii around the x . The energy stored in a capacitor of capacity C and potential V is given by.. What is the final potential difference across each capacitor? thumb_up . An equipotential surface must be perpendicular to the electric field at certain points. So cos cos must be 0, meaning must be 90 90 . The work done by the field can be calculated using the expression: However for equipotential surfaces, V= 0, thus the work done is W = 0. So, there is loss in potential energy. Table of Content ; When an external force does work, such as moving a body from one point to another against a force such as spring force or gravitational force, the work is . Define Equipotential Surface In other terms, an equipotential surface is a surface that exists with the same electrical potential at each point.If any point lies at the same distance from the other, then the sum of all points will create a distributed space or a volume. . Any plane normal to the uniformfield direction is an equipotential surface. d. parallel to the electric field at every point. electrostatics Share Cite It follows that E E must be perpendicular to the equipotential surface at every point. Equipotential Bonding Bar (EBB) Type 3. The particle has started from rest on an equipotential plane of 50 V. After t = 0.0002 sec, the particle is on the equipotential plane of V = 10 volts. C) No work is required to move the negative charge from point A to This problem has been solved! 2. Thus, like the potential energy of a mass in a gravitational field, the electrostatic potential energy of a charge in an electrostatic field is defined. It can be defined as the location of all points in space that have the same potential value. The potential Inside a hollow charged spherical conductor is constant. The entire conductor must be equipotential. 8 An equipotential surface must be A parallel to the electric field at any point. a. oriented 60 with respect to the electric field at every point. Why are conductors equipotential surfaces? Now you are provided with all the necessary information on the equipotential surfaces and their properties and we hope this detailed article is helpful to you. If equipotential points are distributed throughout a space or volume, it is called an equipotential volume. Share Improve this answer Follow answered Oct 12, 2021 at 22:24 Logan R. Kearsley 36.7k 4 87 153 Thank you. In other words, motion along an equipotential is perpendicular to E. One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. What do u mean by equipotential surface? No work is done in moving a charge over an equipotential surface. This implies that a conductor is an equipotential surface in static situations. (Figure 3.5.10) Figure 3.5.10 Two conducting spheres are connected by a thin . Electrical Field on Equipotential Surface, Read More:Electric Field and Charge Important Questions, Read More:NCERT Solutions for Class 12 Physics Chapter 2, Question 2: A charged particle q = 1.4 mC, moves a distance of 0.4 m along an equipotential surface of 10 V. Determine the work done by the field during this motion. An equipotential surface is a circular surface drawn around a point charge. Work would be required to shift a unit test charge in the opposite direction as the component of the field. i.e., potential difference between them is zero. The work required to move a charge between two points in an equipotential surface equals zero. Conceptual Questions What is an equipotential line? Question 1: A positive particle having a charge of 1.0 C accelerates in a uniform electric field of 100 V/m. Surface with constant electrostatic potential values is termed as an equipotential surface. It is a plane section of the three-dimensional graph of the function (,) parallel to the (,)-plane.More generally, a contour line for a function of two variables is a curve connecting points where the . For example, the surface of a conductor in electrostatics is an equipotential surface. It is impossible for two equipotential surfaces to intersect. It can be defined as the locus of all points in the space that have the same value of potential. Uploaded By KeithLeung. Created by Mahesh Shenoy. It is because of the fact that the potential gradient in a direction parallel to an equipotential surface is zero; thus, \(E =\, \frac{{dV}}{{dr}} = 0\). "@type": "Question", Science Physics Q&A Library Starting with the definition of work, prove that at every point on an equipotential surface, the surface must be perpendicular to the electric field there. An equipotential sphere is a circle in the two-dimensional view of this figure. Different equipotential surfaces exist around the point charge, i.e. "acceptedAnswer": { I can see that is due to all the points on the sphere's surface is equidistant from the point charge. . The concentric spheres around a point charge individually represent different equipotential surfaces. Estimate the heat released by the substance in aligning its dipoles along the new direction of the field. TRUE or FALSE? This implies that a conductor is an equipotential surface in static . Related Courses. A Plane Electromagnetic Wave Of Frequency 50 MHztravels in. Equipotential Surface and Its Properties: A surface that has a constant value of potential throughout is known as an equipotential surface. Uncategorized. e. oriented 30 with respect to the electric field at every point. The equipotential surfaces are the planes that are normal to the x-axis in a region around a uniform electric field. For a point charge, the equipotential surfaces are concentric spherical shells. Total dipole moment of all the molecules can be written as, Final potential energy (when = 60), Uf, Change in potential energy = 3 J (6 J) = 3 J. \n. Note that in this equation, E and F symbolize the magnitudes of the electric field and force, respectively. An equipotential surface must be A) parallel to the electric field at every point B) equal to the electric field at every point C) perpendicular to the electric field at every point D) tangent to the electric field at every point E) equal to the inverse of the electric field at every point C) perpendicular to the electric field at every point "name": "Q.2. What is an equipotential surface? When the external force is excluded, the body moves, gaining the kinetic energy and losing an equal quantity of potential energy. An equipotential surface is thus a surface where the potential is the same at every point on the surface. In a uniform electric field, equipotential surfaces must : This question has multiple correct options A be plane surfaces B be normal to the direction of the field C be spaced such that surfaces having equal differences in potential are separated by equal distances D have decreasing potentials in the direction of the field Medium Solution The equipotential surfaces are of concentric spherical shells for a point charge. In the circuit shown, findCif the effective capacitance of the whole circuit is. Embiums Your Kryptonite weapon against super exams! The direction of the electric field is always perpendicular to an equipotential surface; thus, \(E =\, \frac{{dV}}{{dr}} = 0\), and two equipotential surfaces can never intersect each other. Equipotentials simply connect all the points that have the same potential energy (if a particle was . ocean surface must be an equipotential surface of the gravitational field, and because the latter reflects variations due to heterogeneities of density within Earth, so also do the equipotentials. The spacing between equipotential surfaces, by convention, is such that the change in potential is the same for adjacent equipotential surfaces. Equipotential points are all the points present in the space around an electric field with the same magnitude of electric potential. The equipotential surface is said to be a sphere for an isolated point charge. The direction of the electric field is always perpendicular to an equipotential surface. Equipotential surfaces are a useful way to represent the potential distribution in an electric field graphically. Divide the potential energy by the quantity of charge to get the charges electric potential. Two equipotential surfaces can never intersect. There can be no voltage difference across the surface of a conductor, or charges will flow. Can there be a non-zero component of the electric field along an equipotential surface?Ans: No, there can not be a non-zero component of the electric field along an equipotential surface. } Two equipotential surfaces can not intersect.2. Physics 102 Electricity and Magnetism. We can associate equipotential surfaces across a region having an electric field. Write two properties of equipotential surfaces. Each equipotential surface is defined as the set of all points in a specific region of space that shares a common potential value. Also calculate the time taken by the electron to attain a speed of 1.0 c, where c is the velocity of light. In electrostatics, the work done is calculated by: Uis the electric potential energy gained by the charge when it is forced to move in external electric potential. Creative Commons Attribution/Non-Commercial/Share-Alike. It is at the axis between the two dipoles, perpendicular to the plane where the electric potential due to the dipole is zero. The position of an electrically charged object in relation to other electrically charged objects. As 1 mole of the substance contains 6 1023 molecules. The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is called grounding. In domestic premises, the locations identified. However, this contradicts the definition of an equipotential surface, which states that there is no potential difference between any two places on the surface and that no work is necessary to move a test charge over it. For stronger fields, equipotential surfaces are closer to each other! Therefore, at all points, the electric field must be normal to the equipotential surface. An equipotential surface is a three-dimensional version of equipotential lines. For a single charge q(a) equipotential surfaces are spherical surfaces centered at the charge, and(b) electric field lines are radial, starting from the charge if q > 0. These equipotential surfaces are always perpendicular to the electric field direction, at every point. With position vector r from the origin, we want to find the potential at any point P. To do so, we must compute the amount of work required to transport a unit positive test charge from infinity to point P. When Q > 0, the work done on the test charge against the repulsive force is positive. If there were a potential difference from one part of a conductor to another, free electrons would move under the influence of that potential difference to cancel it out. Characteristics of Equipotential Surfaces: 1. But it contradicts the fact that no work is required to move a test charge across the equipotential surface. We can also understand it as: If the direction of the electric field were not normal to the equipotential surface, then it will have a non-zero component along its surface. Consequently, field lines point inwards or outwards from the surface. Thus, no work is required to move a charge from the centre to the surface or across the sphere of such a conductor. The term equipotential is also used as a noun, referring to an equipotential line or surface. The electric potential of an electric dipole is symmetrical at the centre of the dipole. The above figure is (a) Equipotential surfaces for a dipole and (b) Equipotential surfaces with two identical positive charges. [Click Here for Previous year's Questions]. If a test charge q0 q 0 is moved from point to point on an equipotential surface, the electric potential energy q0V q 0 V will remain constant. Procedure for CBSE Compartment Exams 2022, Maths Expert Series : Part 2 Symmetry in Mathematics. Starting with the definition of work, prove that at every point on an equipotential surface the surface must be perpendicular to the electric field there. The charge doesnt gain any energy, as there is no change in electric potential because the surfaces are equipotential. This imaginary surface is along the z-axis if the field is set in an X-Y plane. Electrostatic field of magnitude 106 V m1. Problem 3: Determine the electrostatic potential energy of a system consisting of two charges 7 C and 2 C (and with no external field) placed at (9 cm, 0, 0) and (9 cm, 0, 0) respectively. Calculate the work done by the field throughout this motion.Solution: The expression gives the work done by the field, \(W =\, q.\Delta V\)For an equipotential surface, \(\Delta V = 0\)Thus, the work done, \(W =\, q.0 = 0\)work done is zero. Note that the connection by the wire means that this entire system must be an equipotential. Along with the equipotential surface, it is necessary to consider the work done when we move charge along the surface. The equipotential surface through a point is normal to the electric field at that location for any charge arrangement. 1: An isolated point charge Q with its electric field lines in blue and equipotential lines in green. If there were a potential difference from one part of a conductor to another, free electrons would move under the influence of that potential difference to cancel it out. It follows from Eq. Hence, the entire volume inside must be equipotential. An equipotential sphere is a circle in the two-dimensional view of Figure 7.6. perpendicular to the electric field at every point. No, the work donewill be path independent. Here, V is constant if r is constant. A boy of mass 50kg is standing at one end of a, boat of length 9m and mass 400kg. Determine the distance traveled by the particle. As the field is along x-direction, equipotential surface must be parallel to yz-plane. The amount of work required to transport a unit charge from a reference point to a specific point against the electric field is known as electric potential. Sharma vs S.K. When an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. Theatre Earth Reference Bar (ERB) enclose assembly; 400W x 300H x 77.5D mm; To ensure earthing compliance in line with HTM06-01 and BS7671:2008 section 710, for safe Hospital design reducing the risk of electric shock in patient areas, an Equipotential Bonding Busbar or Earth Bonding Bar (EBB) should be incorporated into the design of the electrical . 1. An isolated point charge Q Q with its electric field lines in blue and equipotential lines in green. Therefore, equipotential surfaces of a single-point charge areconcentric spherically centered at the potential charge. In the above expression, it is observed that if r is constant then V also remains constant. The potential for a point charge is the same anywhere on an imaginary sphere of radius size 12 {r} {} surrounding the charge. However, since I have similar curiosity myself I'm going to try to answer in greater depth. This concept was never stated in the theory part of the book, so I wanted to know more about it. . { Expert Answers: Supplementary or additional equipotential bonding (earthing) is required in locations of increased shock risk. Sort by: What is the word required to move a charge on an equipotential surface?Ans: The work required to move a charge on an equipotential surface is zero. If this is the case, then the correct answer could be (d). Neither q nor E nor d is zero, and so cos must be 0, meaning must be 90.In other words, motion along an equipotential is perpendicular to E.. One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface . The equipotential surfaces around an isolated point charge are in the form of spheres. The equipotential surface direction is from high potential to low potential. Answer sheets of meritorious students of class 12th 2012 M.P Board All Subjects. Points in an electric field that are at the same potential are known as equipotential points and if they are connected by a curve, then it is called an equipotential line. To move a charge from one point to another on the equipotential surface, work is not required. (V= 4 104 V). Compute its acceleration. It is not possible for two equipotential surfaces to intersect with each other as this would contradict how an equipotential surface is defined. c. equal to the electric field at every point. This means that work will be required to move a unit test charge against the direction of the component of the electric field. Equipotential surfaces for a uniform electric field. An equipotential surface must be. Moving a charge between two places on an equipotential surface is always zero. The distance between equipotential surfaces allows us to distinguish between strong and weak fields. "@type": "Answer", This must be the energy released by the substance in the form of heat in aligning its dipoles. An equipotential surface is a surface that has the same value of potential throughout. Featuring some of the most popular crossword puzzles, XWordSolver.com uses the knowledge of experts in history, anthropology, and science combined to provide you solutions when you cannot seem to guess the word. The acceleration of the electron is calculated by: Let t be the time taken by the electron in attaining a final speed of 1.0 c. t = v/a= (0.1c) a= (0.13.1108) (1.81017), Question 4: Can two equipotential surfaces intersect with each other? So my answer is that a conductor is not an equipotential surface if you consider the orbital/quantum effects. No work is needed to move a charge from the centre to the surface. But why does all the points inside the sphere have same potential. The surface, the locus of all points at the same potential, is known as the equipotential surface. For instance consider the map on the right of the Rawah Wilderness in northern Colorado . The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is called grounding. In addition, all metal within 5 feet of the inside of the pool wall must be bonded with the equipment to form the equipotential bonding grid. The surfaces dont intersect the shift form to reflect the new configuration charge.Hence, no two equipotential surfaces can ever intersect. The effective capacitance between two points is. Note that the connection by the wire means that this entire system must be an equipotential. Thus the equipotential lines will be parallel to the plates of the capacitor. For a point charge, the equipotential surfaces are concentric spherical shells. Both have an inverse-square relationship on distance and differ only in the proportionality constants. An equipotential surface has an electric field that is constantly perpendicular to it. Problem 4: 6 A molecule of a substance has a permanent electric dipole moment of magnitude 1029 C m. A mole of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude 106 V m1. When similar potential points are connected by a curve or a line, they are referred to as an . The masses in the expression of gravitational law are replaced by charges in Coulombs law expression. Here, the work done in moving a charge in an equipotential surface is given as: The work done in moving a charge in an electric field is: Hence, the particle has traveled a 0.4 m distance. We choose a handy path along the radial direction from infinity to point P since the work is done is independent of the path. }] A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Every point on a given line is at the same potential. Equipotential Surface is the surface that has a constant value of electrical potential at all the points on that surface. Equipotential surfaces can be shown as lines in two dimensions to provide a quantitative way of viewing electric potential. "name": "Q.1. "@type": "Question", We can associate equipotential surfaces across a region having an electric field. "@type": "Question", Equipotential Surface is the surface that has a constant value of electrical potential at all the points on that surface. "@type": "Answer", For a uniform electric field E, say, along the x-axis, the equipotential surfaces are planes perpendicular to the x-axis, that is planes parallel to the y-z plane as shown in the above figure. we've learned how to visualize electric field by drawing field lines in this video let's explore how to visualize electric potentials and the way to do that or at least one way of doing that is by drawing something called equipotential surfaces so what exactly are these well as the name suggests these are surfaces and these are three dimensional surfaces over which the potential at every point is equal equipotential surfaces let me give an example so if we come over here let's say from this charge i go about two centimeters far away over here there will be some potential at that point let's call that as 10 volt let's imagine that to be 10 volt now if i went 2 centimeters over here from the charge what would the potential there it should also be 10 volts what about 2 centimeters from here that should also be 10 volt in fact i could draw a circle of two centimeters and two set images an example okay and everywhere on that circle the potential would be equal 10 volt so that circle would be an equi-potential surface and since it's a three-dimensional you have to imagine this actually is not a circle but it's a sphere so let me just draw that nicely so i could draw a sphere let's see here it is a sphere and you have to imagine this is a three-dimensional sphere where every on every point of it the potential is 10 volt equal and so this would be my 10 volt equipotential surface can i draw more of course if i go a little farther away maybe two and a half or three centimeters far away i would can draw another sphere that will have another that would be another equipotential surface let me draw that if i go farther away the potential will decrease right so let's say this is another equipotential surface why is this equipotential because every on every point of it the potential is equal and is equal to 7 volt can i draw more yes more spheres every sphere you draw will be an equipotential surface in fact if i if i go a little farther away and i draw another one i might get a nine volt equipotential surface if i go a little farther away and i draw another one i might get an eight volt equipotential surface and so on and so forth now before we continue you may immediately notice that the surfaces are closer here and they're going farther and farther away why is that well it's got something to do with the strength of the electric field close to the charge the field is very strong and that's where the potentials are equipotential surfaces will be closer to each other as we go far away from the charge the field weakens and so the surfaces go further and farther away from each other but why why is it that if the field becomes weaker the equipotential surfaces go farther away can you pause and think a little bit about this all right here's how i like to think about it consider a tiny test charge kept over here on the 10 volt equipotential surface what will happen if i let go of it well electric field will push it and it'll accelerate and will move from this equipotential to another the nine volt equipotential now because the force over here is very strong because you are in a strong electric field region it will accelerate very quickly it will gain kinetic energy very quickly and as a result it will lose potential energy very quickly and it's for that reason in a very short distance it would have reached from 10 volt to 9 volt equipotential surface however what would happen if i were to keep that same test charge over here well now the field is very weak or weaker compared to here and so the force acting on it is very weak and so it will accelerate slowly and so it's going to take more distance for it to pick up the kinetic energy and so it's going to lose potential energies more slowly and as a result it's going to take a longer distance before it reaches uh it loses one volt now and so what do you think will happen for the six volt equipotential it will take even larger distance to reach eq six volts and so it'll be even farther away does that make sense it's kind of like if you take a ball and drop it on say jupiter where the gravitational field is very strong then it will accelerate very quickly and so it will gain kinetic energy very quickly so it will lose potential energy very quickly but on the other hand if you were to drop that same bowling ball on say moon well because the gravitational field is very weak it's going to accelerate very slowly gain kinetic energy very slowly and so therefore lose potential energy very slowly so the weaker field in weaker fields you lose potential very slowly and so the potential surfaces are further away all right let's take another example and i want you to take a shot at drawing equipotential surfaces let's say we have a long infinitely long sheet of charging big sheet of charge which has let's say negative charge then we know we've seen before it produces a uniform electric field can you think of what the equipotential surfaces here would look like can you draw try drawing a few exponential surfaces over here pause the video and think about this use the same approach as we did over here all right just like over here let me go at some distance say about two centimeters from this sheet it'll have some potential because it's a negative charge maybe there is some i don't know negative 10 volt potential now if i go two centimeters from here i should get exactly the same potential as here and the same would be the case over here as well oh that means i can draw connect all these lines and if i do that now my equipotential surface would look somewhat like this so this would be my minus 10 volt equipotential surface i can draw another if i go a little bit farther away maybe i will get another let's say minus 9 volt equipotential surface if i go farther away maybe i get another minus eight volt equipotential surface and so on and so forth over here i hope you agree that the equipotential surfaces will be equidistant because the field lines are all uh the electric field is uniform and again just to reiterate this is not a line this is a surface it's so you have to imagine this in three dimensions and i'll help you visualize that if you could see this in three dimensions so if you look at them in 3d you can now see that now the equipotential surfaces are plane surfaces so over here we've got spheres over here we're getting plane surfaces all right but here's a question these were simple cases but what if we have to draw equipotential surfaces in general what if i have some random electric field line due to like some complicated network of charges something like that i don't know just randomly drawing how would we draw equipotential surfaces then we may not be able to use the same approach like here but what we can try to do is see if there is some geometrical relationship between electric field lines and equipotential surfaces so let's come over here can we see any relationship between these field lines and the potential surfaces if you look very closely you can see that these equipotential surfaces are perpendicular to the field lines and that makes sense right because in general over here the field lines are forming the radius and the radii are always perpendicular to the spheres or circles so here we are seeing that the two are perpendicular to each other hmm let's look it over here hey here also we are seeing that the field lines are perpendicular to the equipotential surfaces interesting so can we say that this is true in general that equipotential surfaces and field lines must always be perpendicular to each other we can't just say that using two examples we could say that might be a coincidence so is this true in general well if you and i were in the same room maybe you would have an interesting dialogue over here but i don't want to take too much time and i'll go ahead and tell you that turns out that this is true in general so let me just write that down equipotential surfaces are always always perpendicular to electric field lines i can just say perpendicular to field or field lines always regardless of how complex the field lines are and again the final question for us in this video is why this is true and i want you to again pause and ponder upon this is a deep question but i'll give you one clue think in terms of contradiction what would happen if the equipotential surfaces were not perpendicular to the field lines what gets broken think a little bit about that like i said it's a deep question don't expect it to get right away and it's okay if you don't get it right away but the idea is just to think a little bit about it before we go forward all right let's see there are multiple ways to think about this uh the way i like to think about is again bring back my test charge so here's my test charge now imagine we move this charge along the equipotential surface say from here to here now because it's an equipotential at every single point the potential is the same that means the potential energy of this test charge will remain the same as you move it right let me write that down no change in potential energy no change in potential energy as you move along the equipotential by definition right okay what does that mean well if the potential energy is not changing it automatically means no work done by the electric field no work by the electric field now think about it for a second why should this be true because whenever electric field does work whether positive work or negative work where automatically potential energy would change for example let's get let's come let's bring back gravity because gravity helps in understanding this what happens when when you drop a ball gravitational field does positive work what happens to the potential energy it loses it what happens when you throw a ball up gravity does negative work what happens to the potential energy it gains it so notice whenever gravity does work this ball would either lose or gain potential energy same would be the case over here if electric field did work the charge would have gained or lost potential energy but we are seeing that it is not changing its potential energy means that as you go from here to here electric field must be doing zero work but how is that possible electric field is definitely pushing on the charges putting a force on the charge and the charge is moving so how can work done be zero oh work done can only be zero if the force and the direction of motion are perpendicular to each other so in short as you move a test charge along the equipotential surface its potential energy should not change that can only happen if the electric field does no work and that can only happen if and only if electric fields are perpendicular to the equipotential surfaces now if you find this a little hard to you know digest this right away it's completely fine it took me also a long time to do that so keep pondering keep thinking about it it'll eventually make sense so long story short this basically means if you have been given some random field lines and if you want to draw equipotential surfaces just start drawing perpendicular drawing them perpendicular to the field lines this is how you might do it and of course nobody's going to ask you to do that but you know or you you usually use computers to do that but that's the idea but equation surface must always be perpendicular to the field line all right let's summarize and i want you to summarize and the way to do that is i'm going to ask you three questions and see if you can explain it to a friend what what are equipotential surfaces that's question one second question why over here these surfaces are going farther and farther apart from each other but over here the surfaces are equidistant and third one why are equipotential surfaces always perpendicular to the field lines, Middle school Earth and space science - NGSS, World History Project - Origins to the Present, World History Project - 1750 to the Present. 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