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.

The points present in an electric field having similar electric potential are called **equipotential points**.

When similar potential points are connected by a curve or a line, they are referred to as an **equipotential line**, and when points lie on a surface, they are called an equipotential surface.

If these points are distributed throughout either volume or space, it is called an **equipotential volume**.

Index

**Work **D**one on Equipotential Surface**

The work done in moving a charge between the two points in an equipotential surface is **zero** since the potential is the same at all points on that surface.

If a point charge is being moved from the point \(A\) having potential \(V_A\) to \(B\) having potential \(V_B\), the work done in moving the charge can be given by,

\(W = q_o(V_A – V_B)\)

As the potential of \(V_A = V_B\), the total work done, \(W = 0\)

**Properties of Equipotential Surface**

The properties of the equipotential surfaces are:

- Two equipotential surfaces
**never intersect**. - The
*electric field*and*equipotential surfaces*are**perpendicular**to each other. - For a
*uniform electric field*, the equipotential surfaces are planes that are normal to the x-axis. - The equipotential surface
**directions from high potential to low potential**. - For a
*point charge*, the equipotential surfaces will be in the form of concentric spherical shells. - In a
*uniform electric field*, the planes normal to the direction of the field are equipotential surfaces. - The potential inside a
*hollow charged spherical conductor*is a*constant*. This is treated as equipotential volume. (No work is done in moving a charge from the center to the surface.) - For an
*isolated point charge*, the equipotential surfaces are in the form of a sphere. I.e., the concentric spheres around the point charge will contain different equipotential surfaces. - The space between the equipotential surfaces allows us to identify strong and weak field regions.

\(E = \frac{-d_v}{d_r} \Rightarrow E \propto \frac{1}{dr}\)

**Example Problems**

**Question 1.** A charged particle (\(q = 2mC\)) moves a distance of 2 m along an equipotential spherical shell of 7 V, what is the work done by the field during this motion.

**Solution.** The work done is given by \(W = -q \Delta V\)

Since, \(\Delta V = 0\)

Therefore, \(W = 0\)

**Question 2.** A positive particle of charge 1.0 C accelerates in a uniform electric field of 10 V/m. The particle started from rest on an equipotential plane of 5 V. After *t* = 0.00002 seconds, the particle is on an equipotential plane of V = 1 volts. Determine the distance traveled by the particle.

**Solution.** We know that, \(W = -q \Delta V\)

\(W = (-1.0 C) (1V – 5V) = 4 J\)

Work done in moving a charge in an electric field: \(W = qEd\)

\(4 = (1.0) (10)d\)

\(d = 0.4m\)

Thus, the distance traveled is 0.4 m.

**FAQs**

**What is an equipotential surface?**A surface having the same potential at every point is referred to as an equipotential surface.

**What is Work done on an Equipotential surface?**The work done in an equipotential surface is Zero.

**What is Equipotential Volume?**Equipotential points that are distributed throughout either volume or space, it is called equipotential volume.

**Equipotential surface for a point?**A point charge will form an equipotential spherical shells.

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