Table of Contents

**Introduction**

The surface which is the location of all points which are at the same potential is known as the equipotential surface. On the equipotential surface, moving a charge from one point to another requires no effort. In other terms, an equipotential surface is one that has the same electric potential at all points. The equipotential surface is the center of all points and has the same potential. To move a charge from one point to another on the equipotential surface, no work is required. Equipotential Points: Equipotential points are the same electric potential points on the electric field. An equipotential line is a line or curve that connects the points. The surface on which the point is located is referred to as the equipotential surface. An equipotential volume is a volume in which the points are filled.

In three-dimensional space, an equipotential region of a scalar potential is frequently an equipotential surface (or potential isosurface), but it can also be a three-dimensional solid (mathematics). The gradient of the scalar potential (and thus its inverse, as in the case of a vector field with an associated potential field) is perpendicular to the equipotential surface everywhere and zero inside a three-dimensional equipotential region.

Electrical conductors are a simple example. If a and b are any two points on or near the surface of a given conductor, and there is no charge flow between the two points, the potential difference between the two points is zero. As a result, an equipotential would include both points a and b because they have the same potential. Using this definition, an isopotential is the location of all points with the same potential.

**Overview**

When an external force acts to do work, such as moving a body from one point to another against a force such as spring force or gravitational force, that work is collected and stored as the body’s potential energy. When the external force is removed, the body moves, gaining kinetic energy and losing a corresponding amount of potential energy. The sum of the kinetic and potential energy is thus conserved. Conservative forces are forces of this type. Two examples of these forces are spring force and gravitational force. An equipotential surface is one that has a fixed potential value at all points on the surface. The potential for a single charge q can be expressed as

V=q⁄4πE_{0}r

It can be seen in the above expression that if r is constant, then V is also constant.

Equipotential surfaces of a single point charge are thus concentric spherical surfaces centered on the charge.

Equipotential surfaces are spherical surfaces centered on the charge for a single charge q, and electric field lines are radial, starting from the charge if q > 0.

The electric field lines for a single charge q are radial lines that begin or end at the charge, depending on whether q is positive or negative. Each electric field is clearly normal to the equipotential surface that passes through that point. For any charge arrangement, the equipotential surface through a point is normal to the electric field at that location. The evidence for this claim is straightforward. If the field is not perpendicular to the equipotential surface, it has a non-zero component along the surface. To shift a unit test charge in the opposite direction as the component of the field, work would be required. This, however, contradicts the definition of an equipotential surface, which states that no potential difference exists between any two points on the surface and that no work is required to move a test charge over it. As a result, the electric field must be normal to the equipotential surface at all times. Equipotential surfaces, in addition to the image of electric field lines around a charge arrangement, provide an additional visual image.

**Properties of Equipotential Surface**

- An equipotential surface has an electric field that is perpendicular to it at all times..
- The intersection of two equipotential surfaces is impossible.
- Equipotential surfaces are concentric spherical shells for a point charge.
- Equipotential surfaces are planes normal to the x-axis given a homogeneous electric field.
- The equipotential surface is oriented from high potential to low potential.
- Inside a hollow charged spherical conductor, the potential is constant.
- Equipotential volume can be used for this. Moving a charge from the centre to the surface requires no effort.
- An isolated point charge’s equipotential surface is a sphere.
- Different equipotential surfaces, i.e. concentric spheres, exist around the point charge.
- Any plane normal to the field direction is an equipotential surface in a homogeneous electric field.
- By measuring the distance between equipotential surfaces, we can distinguish between strong and weak field zones, i.e.

E=-dV/dr ⇒E ∝1/dr

**Problems on Equipotential Surface**

**Q.1: A charged particle (q =1.4 mC) moves 0.4 m along a 10 V equipotential surface.**

**Determine the amount of work done by the field during this motion.**

**Ans:** The expression describes the work done by the field.

W is equal to -qV.

Because V = 0 for equipotential surfaces, the work done is 0 (W = 0).

**Q.2: In a uniform electric field of 100 V/m, a positive particle with a charge of 1.0 C accelerates. The particle began at rest on a 50 V equipotential plane. The particle is on an equipotential plane of V = 10 volts after t = 0.0002 seconds. Determine the particle’s travel distance.**

**Ans:** The work done in moving a charge across an equipotential surface is denoted by

W is equal to -qV.

We get by substituting the values

(-1.0, C) (10V – 50V) W = 40 J

We know that the work involved in moving a charge in an electric field is as follows:

qEd = W

(1.0) (100)d = 40

d is equal to 0.4m.

**Define Equipotential Surface**

An equipotential surface is one that has a fixed potential value at all points on the surface. The equipotential surface is the surface that is the centre of all points and has the same potential. On the equipotential surface, no work is required to move a charge from one point to another.

Also read: **Important Topic of Physics: Potential Difference**

**FAQs**

**1. Is there an electric field tangential to equipotential surfaces?**

**Ans:** No, As we know, potential difference along an electric field = E*d, where E denotes the magnitude of the electric field and d denotes the distance and direction of movement of the electric field from a fixed point. Assume that if there is an electric field along the surface of the Equipotential Surface, there must be some potential difference according to the equation. As a result, the surface is not an equipotential surface. Because of this, there is no field along the tangent to the surface of the equipotential surface.

**2. Which of the following is incorrect about an equipotential surface in a uniform electric field?**

**(a) The equipotential surface is level.**

**(b) The amount of work completed is nil.**

**(c) The equipotential surface has a spherical shape.**

**(d) Electric lines run parallel to the equipotential surface.**

**(c) The equipotential surface has a spherical shape.**

**Ans: **The equipotential surfaces are planes normal to the x-axis that have a uniform electric field along the x-axis. Because the potential at all points on the equipotential surface is constant, the work done to move a charge from one point to another is zero.