Equipotential Surfaces

Introduction:

So, today in this section, we will clear our concepts on the equipotential surfaces. We will go through their definition, properties, and possible issues with the equipotential surfaces. The quick questions that help you clear any possible doubts on the topic are not to miss.

Points in equipotential surfaces

In an equipotential surface, all the points are at the same potential. Hence, no work is required to move a charge from one point to another. Any surface with the same electric potential at different points can be termed the equipotential surface.

The points in an equipotential surface are all at the same potential; all such points are called equipotential points. A line or curve passing through the different equipotential points is called the equipotential line. If the equipotential points are spread over a space or volume, these equipotential points constitute an equipotential volume. The surface containing equipotential points is the equipotential surface.

Work done on an equipotential surface:

The work done is the energy required in moving a charge from one place to another on any surface. The work done on the equipotential surface is zero as all points are at the same electric potential. Hence, it can be represented as:

W = q0(VA –VB)

where:

VA: potential at point A,

VB: potential at point B,

q0: the amount of the charge

Here, as VA –VB is zero, hence W= zero. Thus, the work done on an equipotential surface is zero at all times.

Properties of the equipotential surface:

The characteristic properties of the equipotential surface are:

• The two equipotential surfaces never intersect each other.
• The equipotential surfaces are planes normal to the x-axis for a uniform electric field.
• A hollow charged spherical conductor can be treated as an equipotential surface. This is because the potential inside a hollow charged spherical conductor is constant, and no work is required to move the charge from the center to the surface.
• Any plane normal to the electric field direction having a uniform electric field is an equipotential surface.
• The electric field always lies perpendicular to the equipotential surface.
• The equipotential surfaces are in the shape of concentric spherical shells for any point charge.
• The equipotential surface spacing helps identify the regions of strong and weak fields.
• The equipotential surfaces are in the shape of spheres for the isolated point charges. In other words, the different concentric spheres around the point charge are the different equipotential surfaces only.
• The direction of the equipotential surface is always from the high potential to the low potential.

Problems on an equipotential surface:

After defining the equipotential surface, let us have a look at the top problems on it:

1. Calculate the work done by the field in moving a charged particle of 1.4 mC to 0.4m in an equipotential surface of 10V.

If the charge is moved in an equipotential surface, the work done in moving the 1.4 mC charge to 0.4m in a 10V surface is zero. All points in an equipotential surface are at the same potential.

2. Calculate the distance traveled by the positive charge of 1.0C that started from the rest on an equipotential surface of 50V, and after the 0.0002s, it is on the equipotential surface of 10V.

Here, q= 1.0C

W= 10V-50V= 40J

Hence, W= q*Ed

40= q*Ed

40= (1.0) * (100)* d

Hence, d= 0.4m

Thus, the distance traveled by the charge is 0.4m.

3. There are two 1.0C charges- one positive and one negative resting in a coordinate system with axis (1.0m, 1.0m), (1.0m, 2.0m). Calculate the potential magnitude on the equipotential surface created by the points at coordinates (1.0m, 1.5m) and (1.5m, 1.5m).

Going through the coordinates of the charges, both positions are equidistant for positive and negative charges. So, the potential is zero as the charges are equal and opposite at both points.

Further, the surface formed by these opposite charges is a plane that passes the system, and any addition of the kq/r for any charge keeps it zero at all times. Further, any points on the equipotential surface are at zero potential irrespective of the coordinates.

Conclusion:

These surfaces have the same value of potential at any point and are characterized by a definite set of properties. It should be easy for all our students to solve any numerical or theoretical question on this topic. If not, don’t worry, as you can tune into the Unacademy app or website for quick revision on equipotential surfaces.

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