The diagrams below show regions of equipotentials.

F1 Savita Others 22-8-22 D14

A positive charge is moved from A to B in each diagram.

  1. Maximum work is required to move q in figure (b).
  2. Maximum work is required to move q in figure (c).
  3. In all the four cases the work done is the same.
  4. Minimum work is required to move q in figure (a).

Answer (Detailed Solution Below)

Option 3 : In all the four cases the work done is the same.
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Detailed Solution

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Concept:

Work done in moving the charge from point A  to point B depends upon the potential difference between the points and is independent of the path followed by the charge.

Formula to calculate work done in moving the charge from A to B is:

W = Q ΔV

where Q is a charge, ΔV is the difference between the potential difference between two points i.e., A and B.

An equipotential surface is defined as the region in space that has the same potential at every point. 

Equipotential lines are used to represent equipotential surfaces of two-dimensional.

Equipotential surfaces are always perpendicular to electric field lines. Conductors in static equilibrium are equipotential surfaces. 

Work done in moving charge on the equipotential surface is zero.

Calculation:

Work done w = qΔ V

ΔV is the same in all the cases so the work done will be the same in all the cases.

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