an equipotential surface must be

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Date: 12/12/2022

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 . "acceptedAnswer": { 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. Add the potential due to each charge to calculate the potential due to a collection of charges. Every point on a given line is at the same potential. Here we explore the consequences of charge being able to move inside a conductor, and where the electric fields po. thumb_up . An equipotential surface must be. The equipotential surfaces are the planes that are normal to the x-axis in a region around a uniform electric field. If there is an . No tracking or performance measurement cookies were served with this page. La surface du conducteur est une surface quipotentielle pour ce champ. Inside a conductor E=0 everywhere, = 0 and any free charges must be on the surfaces. Thus, the work required to move a charge between two points in an equipotential surface equals zero. 2. Characteristics of Equipotential Surfaces: 1. 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. If a point charge is moved from point VY to VZ, in an equipotential surface then the work done in the moving point charge can be calculated using the following equation: As the value of VY - Vz is zero, the total work done W = 0. Equipotential surfaces are a useful way to represent the potential distribution in an electric field graphically. There can be no voltage difference across the surface of a conductor, or charges will flow. Ltd. All Rights Reserved, Equipotential, Equipotential Surfaces, Work, Electric Field, Electric Charge, Electric Potential, Work, Get latest notification of colleges, exams and news, Magnitude of Electric Field on Equipotential Surface, Electric Field and Charge Important Questions, NCERT Solutions for Class 12 Physics Chapter 2, A conducting sphere of radius R=20cm is given a charge Q, A metallic sphere is placed in a uniform electric field. This implies that a conductor is an equipotential surface in static situations. Equipotential surfaces for a point charge are concentric spherical shells. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'. Any infinitesimal path can be broken down into two perpendicular displacements: one along to r and one perpendicular to r. The work donerelation to the latter will be zero. The equipotential surface through a point is normal to the electric field at that location for any charge arrangement. }. Therefore the work done to move a charge from one point to another over an equipotential surface is zero. 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. The potential will remain the same on this surface. As shown in the figure, chargesare placed at the vertices. Electrostatic field of magnitude 106 V m1. (m = 9.1 10-31 Kg, e = 1.6 10-19 Coulomb and c = 3 108 m/s)(3 marks). The Great Soviet Encyclopedia, 3rd Edition (1970-1979). "acceptedAnswer": { A positively charged particle having a charge \(q = 1.0{\rm{C}}\) accelerates through a uniform electric field of \(10\,{\rm{V/m}}\). Problem 1: Calculate the potential at a point P due to a charge of 4 107 C located 9 cm away. The electric fields strength is determined by the electric potential. Equipotential surfaces allow an alternative visual image in addition to the image of electric field lines around a charge arrangement. An equipotential surface must be A. tangent to the electric field at every point. For a point charge, the equipotential surfaces are concentric spherical shells. The potential is the same across each equipotential line, implying that no work is required to move a charge along one of those lines. Problem 5: Write the properties of Equipotential Surface. Work is required to move a charge from one point to another in a given region. Equipotential Surface is the surface that has a constant value of electrical potential at all the points on that surface. The spacing between equipotential surfaces, by convention, is such that the change in potential is the same for adjacent equipotential surfaces. The clue "Equipotential surface of the Earth" was last spotted by us at the Crossword Champ Pro Crossword on November 22 2018. 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. TRUE or FALSE? Draw the equipotential surface around an electric dipole.Ans: The equipotential surface can be represented as: Q.4. An equipotential surface is one that has the same potential value throughout. Would you please write me how to figure out which is the reason? 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. Then the work done can be given as: Since the surface is equipotential, \({{V_B} = {V_A}}\), We know that at every point on an equipotential surface, electric field lines are perpendicular to it. 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 In other words it can be defined as - The surface which is the locus of all the points having same electrostatic potential is called equipotential surface. Find out its acceleration. These equipotential surfaces are always perpendicular to the electric field direction, at every point. At point charge +q, all points with a distance of r have the same potential. "text": "Ans: The work required to move a charge on an equipotential surface is zero." ", No, the work donewill be path independent. 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. Note that the connection by the wire means that this entire system must be an equipotential. An isolated point charge Q Q with its electric field lines in blue and equipotential lines in green. Each equipotential surface is defined as the set of all points in a specific region of space that shares a common potential value. Share Improve this answer Follow answered Oct 12, 2021 at 22:24 Logan R. Kearsley 36.7k 4 87 153 Thank you. It can be defined as the locus of all points in the space that have the same value of potential. For an equipotential surface, the work done to move a charge is always zero because the potential at each and every point is the same. The particle moves on an equipotential plane of \(V = 1\,{\rm{V}}\)after \(t = 0.0002{\rm{s}}\). It is impossible for two equipotential surfaces to intersect. School Camosun College; Course Title PHYS 104; Type. For a point charge, the equipotential surfaces are concentric spherical shells. Table of Content It is impossible for two equipotential surfaces to intersect. e. oriented 30 with respect to the electric field at every point. The electric field is always perpendicular to an equipotential surface. While a capacitor remains connected to a battery, a dielectric slab is slipped between the plates..[, The electron is accelerated through a potential difference of 10 V. The additional energy acquired by the electron is. Question 3: An electron of mass m and charge e is released from rest in a uniform electric field of 106 N/C. 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 . Take \(m = 9.1 \times {10^{ 31}}{\rm{kg}},\,e = 1.6 \times {10^{ 19}}{\rm{C}}\)and \(c = 3 \times {10^8}\,{\rm{m/s}}\).Solution: Force on electron, \(F = eF = 1.6 \times {10^{ 19}} \times {10^6} = 1.6 \times {10^{ 13}}{\rm{N}}\)Acceleration of the electron: \(a = \frac{F}{m} = \frac{{1.6 \times {{10}^{ 13}}{\rm{N}}}}{{9.1 \times {{10}^{ 31}}{\rm{Kg}}}}\)Thus, \(a = 1.8 \times {10^{17}}\,{\rm{m/}}{{\rm{s}}^{\rm{2}}}\)It is given that the initial velocity of the electron, \(u = 0\)After a time, \(t\), the final velocity, \(v = 0.1c\)Using the equation of motion,\(v = u + at\)\(t = \frac{v}{a} = \frac{{0.1c}}{{1.8 \times {{10}^{17}}}} = \frac{{0.1 \times 3 \times {{10}^8}}}{{1.8 \times {{10}^{17}}}}\)\(t = 1.7 \times {10^{ 10}}{\rm{s}}\). No work is needed to move a charge from the centre to the surface. 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. For stronger fields, equipotential surfaces are closer to each other! Substituting the cave in the above expression, Problem 2: Obtain the work done in bringing a charge of 2 109 C from infinity to point P. Does the answer depend on the path along which the charge is brought? Equipotential Bonding Bar (EBB) Type 3. (Figure 3.5.10) Figure 3.5.10 Two conducting spheres are connected by a thin . The direction of the field is suddenly changed by an angle of 60. Equipotential surfaces have equal potentials everywhere on them. So, there is loss in potential energy. Q.1. The effect of this negative voltage can now be described in terms of a set of negative equipotential surfaces that run through the hole in the grid cap. 2010 The Gale Group, Inc. In an equipotential surface, if a point charge is transported from point A have potential energyVA to point B have potential energy VB, the work done to move the charge is given by. A surface on which at each and every point potential is the same is called an equipotential surface. 4. "@type": "FAQPage", A boy of mass 50kg is standing at one end of a, boat of length 9m and mass 400kg. When equipotential points lie on a surface, it is called equipotential surface. By definition, potential difference between two points B and A = work done in carrying a unit positive charge from A to B. 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 . 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? Multi Patient Earth Reference Bar (ERB) enclose assembly; 300W x 400H 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 . "@type": "Question", Can two equipotential surfaces intersect? Literature. Is it ok to start solving H C Verma part 2 without being through part 1? . "acceptedAnswer": { This implies that a conductor is an equipotential surface in static . An equipotential surface is a surface that has the same value of potential throughout. Work done in an electric field, W = q V a - V b Here, The expression for the electrostatic potential energy is. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. Coulomb force is a conservative force between two (stationary) charges. A surface with a fixed potential value at all locations on the surface is known as an equipotential surface. 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. Take Q to be positive. The relationship between the angular velocity, A circular disc is rotating about its own axis. Creation of equipotential surfaces. 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. Thus the equipotential lines will be parallel to the plates of the capacitor. We choose a handy path along the radial direction from infinity to point P since the work is done is independent of the path. Consequently, field lines point inwards or outwards from the surface. },{ It is not possible for two equipotential surfaces to intersect with each other as this would contradict how an equipotential surface is defined. When the external force is excluded, the body moves, gaining the kinetic energy and losing an equal quantity of potential energy. b. equal to the inverse of the electric field at every point. Moving a charge between two places on an equipotential surface is always zero. If this is the case, then the correct answer could be (d). This means that work will be required to move a unit test charge against the direction of the component of the electric field. An equipotential surface is a three-dimensional version of equipotential lines. (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. "text": "Ans: An equipotential surface is a surface that has the same value of potential throughout." Q.5. The surface that forms the locus of all points that are at the same potential forms the equipotential surface. The electric field at each place is clearly normal to the equipotential surface that passes through that point. The equipotential surface gets further apart because as the distance from the charge increases the potential decreases. Equipotential points are all the points present in the space around an electric field with the same magnitude of electric potential. For a uniform electric field, the equipotential surfaces are planes normal to the x-axis. }] In other words, any surface with the same electric potential at every point is termed as an equipotential surface. The equipotential surface is said to be a sphere for an isolated point charge. Sharma vs S.K. Also calculate the time taken by the electron to attain a speed of 1.0 c, where c is the velocity of light. Moving a charge from the center to the surface requires no work done. The particular equipotential surface that coincides over the oceans with unperturbed mean sea level constitutes the geoid. 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 energy stored in a capacitor of capacity C and potential V is given by.. What is the final potential difference across each capacitor? Q3. Voltage rating of a parallel plate capacitor is, A bar magnet is10 cmlong is kept with its north. And as there is no change in energy, no work is done. 8 an equipotential surface must be a parallel to the. We are not permitting internet traffic to Byjus website from countries within European Union at this time. Properties of Equipotential Surface The electric field is always perpendicular to an equipotential surface. },{ The equipotential surfaces are of concentric spherical shells for a point charge. The direction of the equipotential surface is from high potential to low potential. Equipotential lines are always perpendicular to electric field lines. Physics 102 Electricity and Magnetism. The potential is constant inside a hollow charged spherical conductor. 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. The electric field lines are perpendicular to the equipotential lines because they point radially away from the charge. An electric dipole consists of two charges of equal magnitude but opposite polarity. Substitute the value in the above expression. The equipotential surfaces around an isolated point charge are in the form of spheres. An equipotential surface has an electric field that is constantly perpendicular to it. 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 If equipotential points are distributed throughout a space or volume, it is called an equipotential volume. When similar potential points are connected by a curve or a line, they are referred to as an . Work done in an equipotential field is given by. 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. An equipotential sphere is a circle in the two-dimensional view of this figure. So my answer is that a conductor is not an equipotential surface if you consider the orbital/quantum effects. It follows from Eq. The entire conductor must be equipotential. Thus, is a point charge \(q\) is moved from a point \(A\) to point \(B\) such that potential at \(A\) is \({V_A}\) and potential at \(B\) is \({V_B}\)across an equipotential surface. The surfaces dont intersect the shift form to reflect the new configuration charge.Hence, no two equipotential surfaces can ever intersect. This can be treated as equipotential volume. The masses in the expression of gravitational law are replaced by charges in Coulombs law expression. The charge doesnt gain any energy, as there is no change in electric potential because the surfaces are equipotential. The electric intensity E is always perpendicular to the equipotential surfaces. The points present in an electric field having similar electric potential are called equipotential points.. Estimate the heat released by the substance in aligning its dipoles along the new direction of the field. Write two properties of equipotential surfaces.Ans: Properties of equipotential surfaces are:1. Any plane normal to the uniformfield direction is an equipotential surface. A solid conducting sphere, having a chargeQ, is surrounded by an uncharged conducting hollow .. But it contradicts the fact that no work is required to move a test charge across the equipotential surface. However, since I have similar curiosity myself I'm going to try to answer in greater depth. electrostatics Share Cite In equation form, this means that the work done is 0: W =-U =-q0V = 0 W = - U = - q 0 V = 0. For example, the surface of a conductor in electrostatics is an equipotential surface. The direction of the equipotential surface is from the region of higher potential to the region of lower potential. Related Courses. . 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A single point charge of the equipotential surface are concentric spherical surfaces centered at the charge. a. oriented 60 with respect to the electric field at every point. In the figure shown below, the charge on the left plate of the 10F capacitor is 30C, In The Figure Shown After The Switch S Is Turned from postion a to b. So W = - U. "text": "Ans: No, there can not be a non-zero component of the electric field along an equipotential surface." Equipotential surface is that surface at every point of which electric potential is same. Conceptual Questions What is an equipotential line? i.e., potential difference between them is zero. "@type": "Answer", d. parallel to the electric field at every point. We can identify strong or weak fields by the spacing in between the regions of 1equipotential surfaces, i.e. Therefore, equipotential surfaces of a single-point charge areconcentric spherically centered at the potential charge. 8 An equipotential surface must be A parallel to the electric field at any point. 2. As a result of the EUs General Data Protection Regulation (GDPR). An equipotential surface is a circular surface drawn around a point charge. 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. The position of an electrically charged object in relation to other electrically charged objects. We can identify strong or weak fields by the spacing in between the regions of equipotential surfaces. Q.2. The properties possessed by equipotential surfaces are mentioned below: If electric field lines are present in an n-dimensional space, then the equipotential surface is perpendicular to this plane. } "name": "Q.1. Write two properties of equipotential surfaces. Q.3. In the circuit shown, findCif the effective capacitance of the whole circuit is. (2 marks). 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. 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. B. perpendicular to the elec Get the answers you need, now! Equipotential Bonding Bar (EBB) Type 2. (Figure 3.5.10) Figure 3.5.10 Two conducting spheres are connected by a thin . Conceptual Questions 1: What is an equipotential line? 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 . Therefore, at all points, the electric field must be normal to the equipotential surface. The component of the electric field parallel to the equipotential surface is zero. As we have the formula of potential as v= kq/r. Electric potential is a scalar quantity. Goyal, Mere Sapno ka Bharat CBSE Expression Series takes on India and Dreams, CBSE Academic Calendar 2021-22: Check Details Here. Somewhere between these negative equipotentials and the positive ones produced by the accelerating voltage is a zero equipotential surface that terminates at the filament. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. I can see that is due to all the points on the sphere's surface is equidistant from the point charge. Equipotential volume can be used to this. Why is the electric field always at right angles to the equipotential . 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. Strong and weak fields can be identified using the space between equipotential surfaces i.e. For a single charge q, the potential can be calculated using the following formula. Why are conductors equipotential surfaces? Uncategorized. 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. 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. For instance consider the map on the right of the Rawah Wilderness in northern Colorado . Some equipotential surfaces for (a) a dipole, (b) two identical positive charges. For a uniform electric field, the equipotential surfaces are planes normal to the x-axis. A negative charge is moved from point A to point B along an equipotential surface. Find the time taken by an electron to attain a speed of \(0.1c\), where \(c\) is the velocity of light. An equipotential surface is a surface that has the same value of potential throughout. Let us read further to determine the properties of equipotential surfaces. An equipotential surface is a three-dimensional version of equipotential lines. CBSE invites ideas from teachers and students to improve education, 5 differences between R.D. Electric field is normal to the equipotential surfaces. Question. A) The negative charge performs work in moving from point A to point B. Note that the connection by the wire means that this entire system must be an equipotential. Procedure for CBSE Compartment Exams 2022, Maths Expert Series : Part 2 Symmetry in Mathematics. Regions of the . ", This implies that the electric field is perpendicular to and The word "Equipotential" is a combination of "Equal" and "Potential". So you need to do more work with the other two components that are given to you. A Plane Electromagnetic Wave Of Frequency 50 MHztravels in. 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. It is possible only when the other end of the field lines are originated from the charges inside. 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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