Equipotential Surface

When an external force does work, such as moving a body from one point to another against a force such as spring force or gravitational force, the work is accumulated and stored as the body’s potential energy. When an external force is eliminated, the body moves, gaining and losing kinetic and potential energy in equal proportions. As a result, both the entire kinetic and potential energy are preserved. Conservative forces are those who fall within this category. These forces include spring force and gravitational force.

Equipotential surface – Definition

The term “Equipotential” is derived from the words “Equal” and “Potential.” An equipotential surface is one that has the same potential value throughout. It can be defined as the location of all points in space that have the same potential value. We can connect equipotential surfaces in a region with an electric field.

Because any surface with the same electric potential at every point is referred to as an equipotential surface. As a result, the work required to move a charge from one point to another across an equipotential surface is zero. Equipotential points are all points in space that have the same magnitude of electric potential as an electric field.

When these points are connected by a curve or a line, this is referred to as an equipotential line, and when these points are located on a specific surface, this is referred to as an equipotential surface.

Equipotential surface work done

Because the potential is the same at all places on an equipotential surface, the effort done in transporting a charge between two spots is zero. If a point charge is transferred from point A with potential VA to point B with potential VB, the work done in transporting the charge may be given by,

W=q0 (VA  – VB)

Because the potential of VA = VB, the total work done, W=0.

Properties

The following are the characteristics of equipotential surfaces:

• The electric field is always perpendicular to the surface of an equipotential potential.

• Two equipotential surfaces will never meet.

• Equipotential surfaces are concentric spherical shells for a point charge.
• Any plane normal to the field direction is an equipotential surface in a homogeneous electric field.

• Equipotential surfaces are planes normal to the x-axis in a homogeneous electric field.

• The potential within a hollow charged spherical conductor remains constant. It may be thought of as an equipotential volume. Moving a point charge from the centre to the surface requires no labour.

• The equipotential surface moves from high potential to low potential.

• The equipotential surface for an isolated charge is a sphere. This translates to concentric spheres.

• This indicates that distinct equipotential surfaces exist in concentric circles around the charge.

• We can locate locations with a strong and weak field by looking at the space between equipotential surfaces.

Equipotential Surface Formula 

In all cases, equipotential lines are perpendicular to electric field lines. 

W = qV 

W = Fd cos / qEd cos = 0 

It is worth noting that in the above equation, E and F represent the magnitudes of the electric field strength and force, respectively.

Electric Field and Equipotential surface

We know that electric field lines are perpendicular to an equipotential surface at every point. Because the potential gradient in the direction parallel to an equipotential surface is zero, E=–dV/dr=0.

The electric field component parallel to the equipotential surface is zero. We may also think of it this way: If the electric field’s direction is not normal to the equipotential surface, it will have a non-zero component along its surface.

This indicates that labour will be necessary to move a unit test charge in the opposite direction as the electric field component. However, this contradicts the fact that moving a test charge across the equipotential surface requires no labour. As a result, at all places, the electric field should be normal to the equipotential surface.

Conclusion 

Equipotential surface is one that has the same potential value throughout. Because any surface with the same electric potential at every point is referred to as an equipotential surface. As a result, the work required to move a charge from one point to another across an equipotential surface is zero. Because the potential is the same at all places on an equipotential surface, the effort done in transporting a charge between two spots is zero. The electric field is always perpendicular to the surface of an equipotential potential. Any plane normal to the field direction is an equipotential surface in a homogeneous electric field. The equipotential surface for an isolated charge is a sphere. Because the potential gradient in the direction parallel to an equipotential surface is zero, E= dV/dr=0.