Q.What is an equipotential surface? Show that the electric field is always normal to an equipotential surface.
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An equipotential surface is a surface on which the electric potential has exactly the same value at every point; for an isolated point charge these surfaces are concentric spheres centred on the charge (since V = kq/r depends only on distance), and for a uniform field they are flat parallel planes perpendicular to the field direction. Two properties follow directly from the definition. First, moving a charge between any two points on the same equipotential surface requires exactly zero net work, since the potential (and hence the potential difference) between those two points is zero. Second, the electric field is always exactly perpendicular to the equipotential surface passing through any given point -- if the field had any component along the surface, that component would do work moving a ch …
An equipotential surface has the same potential everywhere on it, so no work is done moving a charge along it — and since work done equals q0E⋅dl, this forces the electric field to be perpendicular to the surface at every point. …
On an equipotential surface V is constant everywhere, so moving a test charge along the surface does zero work — which is only possible if E has no component along the surface, i.e. E is everywhere normal to it.
An equipotential surface is defined as a surface at every point of which the electric potential has the same value.
Proof that E ⊥ equipotential surface: Let a test charge q₀ be displaced by a small vector dl along the equipotential surface, from one point to a neighbouring point on the same surface. The work done by the electric field is
dW = q₀E·dl = q₀(E cosθ) dl
But since both points lie on the same equipotential surface, the potential does not change, so dV = 0, and since dW = −q₀dV = 0, we get
E·dl = 0 ⟹ E cosθ = 0 (as E, dl ≠ 0) ⟹ θ = 90°
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Showing the 12 most recent of 15 on this concept.
- CBSE 2026Set V11 markMCQQ.The equipotential surfaces of an isolated point charge are :(a) Coaxial cylindrical surfaces(b) Plane surfaces parallel to each other(c) Concentric spherical surfaces centred at the charge(d) Spherical surfaces but not centred on the charge
›Reveal solutionSolution
(c) Concentric spherical surfaces centred at the charge …
- CBSE 2026Set ANNUAL1 markMCQQ.The angle between equipotential surface and electric field lines is(a) 180°(b) 90°(c) 45°(d) 0°
›Reveal solutionSolution
Electric field lines are normal to equipotential surfaces everywhere, so the angle between them is always 90 degrees.
An equipotential surface is one on which potential V is constant, so no work is done in moving a charge along it (W = q(V2-V1) = 0). If the field had any component along the surface, that component would do work in moving a charge along …
- CBSE 2026Set ANNUAL1 markMCQQ.Equipotential surface at a large distance from a collection of charge whose total sum is not zero are –(a) ellipsoids(b) planes(c) paraboloids(d) spheres
›Reveal solutionSolution
Far away, any localized charge distribution with nonzero total charge looks like a point charge.
At a large distance from a collection of charges whose total (net) charge is not zero, the finer details of the actual charge distribution become negligible, and the distribution behaves effectively like a single point charge equal to the total charge, located roughly at its "centre". The equipotential surfaces of a point ch …
- CBSE 2026Set ANNUAL1 markMCQQ.Which of the following statement is/are true for equipotential surface ?(a) The potential is different for different equipotential surfaces.(b) Electric field must always be normal to equipotential surface.(c) Work done to move a charge between any two points is zero.(d) All of the above
›Reveal solutionSolution
All three listed statements about equipotential surfaces are individually true, so the correct choice is that all of the above hold.
Working
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Different equipotential surfaces correspond to different potential values. By definition, each equipotential surface is the locus of points at one particular potential; a different surface (further/closer to the source) is at a different potential value.
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The electric field is always normal to an equipotential surface. If E had any component along the surface, it would do work moving a charge along that surface, changing its potential energy -- contradicting the surface being at constant potential. So E must be entirely perpendicular to it.
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- CBSE 2025Set X11 markMCQQ.Equipotential surfaces for an isolated point charge are __________ in shape.(a) spherical(b) planar(c) cylindrical(d) conical
›Reveal solutionSolution
(a) spherical. The potential of an isolated point charge is V=4πε01rq, which has the same value at all points a distance r from the charge. The locus of cons …
- CBSE 2025Set ANNUAL1 markQ.Can two equipotential surfaces cross each other?
›Reveal solutionSolution
If two equipotential surfaces intersected, the point of intersection would have to be at two different potentials at once, which is impossible; it would also mean the electric field has two directions at that point, which is equally impossible.
Each equipotential surface is, by definition, a surface on which the electric potential has one single fixed value everywhere on it.
If two equipotential surfaces at different potentials (say V1 and V2, with V1 not equal to V2) were to cross at some point P, then P would simultaneously have potential V1 (being on the first surface) and potential V2 (being on the second) - a contradiction, since a point can have only one value of potential.
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- CBSE 2025Set ANNUAL1 markMCQQ.The angle between the electric lines of force and the equipotential surface is(a) 0°(b) 45°(c) 90°(d) 180°
›Reveal solutionSolution
Electric field lines are always perpendicular to equipotential surfaces.
An equipotential surface is one on which the potential V is the same everywhere, so moving along it does no work: dV=−E⋅dl=0 for any displacement dl on the surface. Since E is generally non-zero, this requires E⊥dl, i.e., the field (and hen …
- CBSE 2025Set ANNUAL1 markQ.Figure below shows the equipotential surfaces for two charges q₁ and q₂. Identify the nature of charges q₁ and q₂.
›Reveal solutionSolution
Only like charges give equipotential surfaces that merge into a single closed peanut/dumbbell-shaped surface enclosing both charges - unlike charges never do.
For unlike (opposite-sign) charges, e.g. a dipole, the equipotential value V=0 occurs on the whole perpendicular-bisector plane between them, which is an open, unbounded surface, not a closed loop. Any closed equipotential surface for a non-zero potential value stays wrapped around one charge only - it can never merge with the loop of the other charge, because the sign of the potential contributed by the two charges is opposite.
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- CBSE 2024Set ANNUAL1 markQ.Draw an equipotential surface for a positive charge (q > 0).
›Reveal solutionSolution
For an isolated positive point charge, potential depends only on distance from the charge, so every surface of constant distance (a sphere centred on the charge) is an equipotential surface.
The potential due to a point charge q at a distance r is:
V=4πε01rq
Since V depends only on r, every point at the same distance r from the charge is at the same potential. So the equipotential surfaces are concentric spheres centred on the charge.
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- CBSE 2024Set ANNUAL1 markMCQQ.A charge of 100 μC is placed at the centre of a circle of radius 5 m. Work done in moving a unit positive charge around the circumference of the circle once is(a) 500 J(b) 20 J(c) 0.05 J(d) 0 J.
›Reveal solutionSolution
Work done by a conservative (electrostatic) field around any closed path is always zero — the charge returns to its starting point, so its potential energy is unchanged.
The charge of 100 μC at the centre sets up a radially symmetric electric field. As the unit positive charge is carried once around the circumference, at every point on the circle the potential due to the central charge is the same, V=kq/r (constant, since r = 5 m throughout).
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- CBSE 2022Set ANNUAL1 markQ.What is an equipotential surface?
›Reveal solutionSolution
A surface where potential is constant everywhere; no work is done moving a charge along it.
An equipotential surface is defined as a surface at every point of which the electric potential is the same. Since the potential does not change as we move from one point to another on such a surface, no work is done in moving a test charge along it (W=q(VA−VB)=0 since VA=VB). This also means the electric field is always perpendicular to an equipotential surface at every point — if it had a component along the surface, work would be done moving a charge along that component, contradicting V being constant. For a single …
- CBSE 2020Set ANNUAL1 markQ.The angle between electric line of force and equipotential surface is ____. (Fill in the blank.)
›Reveal solutionSolution
Electric field lines always cut equipotential surfaces at right angles (90°).
An equipotential surface is one on which every point is at the same electric potential; no work is done in moving a charge along such a surface. Since the electric field E=−∇V points in the direction of the steepest decrease of potential, and there is no change in potential along an equipotential surface, the field must have zero component along the surface — i.e., it can only point perpendicular to it. If the field had any component along the sur …
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