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medium difficulty9 min

Equipotential Surfaces

An equipotential surface is a surface on which every point has the same electric potential.

In one line: Same potential means no potential difference; no potential difference means no work along the surface.

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Understand it

No work is done in moving a charge along an equipotential surface because the potential difference between any two points on it is zero. Electric field lines are always perpendicular to equipotential surfaces. Where equipotential surfaces are closer together, the electric field is stronger because potential changes more rapidly with distance.

Example

For an isolated point charge, equipotential surfaces are concentric spheres centred on the charge. In a uniform electric field, equipotential surfaces are parallel planes perpendicular to the field.

Formula and rule

W = q(VB - VA).

On an equipotential surface, VB = VA, so W = 0.

The field-potential relation is E = -dV/dr in one-dimensional form, showing that closer equipotential surfaces indicate stronger field.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A charge of 5 microcoulomb is moved from A to B on the same equipotential surface where VA = VB = 200 V.

  1. 1W = q(VB - VA) = 5 × 10−6(200 - 200) = 0 J.
  2. 2The result does not depend on the path chosen along that surface.

Method you can reuse

Check whether the two points have the same potential; use W = q delta V; draw field lines perpendicular to the surface; compare spacing of surfaces for field strength; avoid assigning a direction to potential itself.

Sketch it in your answer

Draw equipotential surfaces as concentric circles around a point charge in a plane section, with radial electric field lines crossing them at 90 degrees. For a uniform field, draw equally spaced parallel equipotential lines perpendicular to straight field lines.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the work done in moving a charge along an equipotential surface?

Think first, then show answer
The work done is zero because all points on the surface have the same potential, so the potential difference is zero and W = q delta V = 0.

Common wrong answer

Saying work is small but not zero is wrong when both points are on the same equipotential surface.

Don't mix this up

Students often draw electric field lines tangent to equipotential surfaces. Field lines must cut equipotential surfaces at right angles.

Exam tip

In diagram questions, mention both facts: work done along an equipotential surface is zero, and electric field is normal to the surface.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions ask students to draw equipotential surfaces, explain why no work is done along them, compare field strength using spacing, or identify the direction of electric field from an equipotential diagram.
  1. 1

    Enough for 1 mark

    An equipotential surface is a surface on which every point has the same electric potential.

  2. 2

    Add for 2 marks

    Example: For an isolated point charge, equipotential surfaces are concentric spheres centred on the charge. In a uniform electric field, equipotential surfaces are parallel planes perpendicular to the field.

  3. 3

    Add for 3 marks

    No work is done in moving a charge along an equipotential surface because the potential difference between any two points on it is zero.

Practice

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