Equipotential Surfaces

Because the electric potential is constant everywhere on an equipotential surface, the PE of a charged body is constant at all positions on the surface. This demonstrates that the amount of work required to move a charged body between two places on an equipotential surface is zero. Electric field lines are perpendicular to the surface at every point on the equipotential surface. This is due to the fact that the potential gradient in any direction parallel to the surface is zero, and so the component electric parallel to the equipotential surface is also zero.

Between two (stationary) charges, the Coulomb force is a conservative force. Both have an inverse-square relationship on distance, with the proportionality constants being the only difference. The masses in the formulation of gravitational law are substituted by charges according to Coulomb’s law, The electrostatic potential energy of a charge in an electrostatic field is, therefore, determined, just like the potential energy of a mass in a gravitational field. 

The effort done (by an external entity) in constructing the charges at their positions is the potential energy contained in a system of charges. At p1, p2, the potential energy of two charges g1, g2 is given by the distance p12. A charge q has Vq potential energy in an external potential V(r). In a homogeneous electric field E, the potential energy (–p*E) of a dipole moment.

Work done on an equipotential surface

The work done happens while moving a charge between the two points in an equipotential surface is zero. If a point charge is moved from the point Va to Vb in an equipotential surface, the work done in moving the charge can be given by, W = Qo(Va –Vb)

The equipotential surface of a point charge

For an isolated point charge, the equipotential surface is a sphere. i.e. concentric spheres around the point charge are different equipotential surfaces. In a uniform electric field, any plane normal to the field direction is an equipotential surface.

Work Done in Equipotential Surface

Moving a charge between two places on an equipotential surface is always zero. In an equipotential surface, if a point charge is transported from point A having potential energy VA to point B having potential energy VB, the work done to move the charge is given by

W = q(VA –VB) = 0

Because VA – VB = 0, 

The total work done W is 0.

Properties of an equipotential surface:

· Electric field lines are always perpendicular to an equipotential surface.

· Work done in moving an electric charge from one point to another on an equipotential surface is zero.

· Equipotential surfaces for a point charge are concentric spherical shells.

· For a uniform electric field, the equipotential surfaces are normal to the plane.

· The equipotential surface is directed from high potential to low potential.

· The potential inside a hollow charged spherical conductor is constant.This can be done using equipotential volume. Moving a charge from the center to the surface requires no work done.

· The equipotential surface around an isolated point charge is a sphere. Different equipotential surfaces exist around the point charge, i.e. concentric spheres.

·  Any plane normal to the uniform field direction is an equipotential surface.

· The distance between equipotential surfaces allows us to distinguish between strong and weak fields.

Electric Potential

The amount of work required to transport a unit charge from a reference point to a specific

When an object relocates against an electric field, it gains energy that is referred to as electric potential energy. Divide the potential energy by the quantity of charge to get the charge’s electric potential. The electric field’s strength is determined by the electric potential. It is unrelated to whether or not a charge should be placed in the electric field. Electric potential is a scalar quantity. At point charge +q, all points with a distance of r have the same potential.

AAn object’s electric potential is determined by the following factors:

· An electric charge.

· The position of an electrically charged object to other electrically charged objects.

 CONCLUSION

Equipotential Surfaces are the ones that have an equal Electric Potential all over them. It is said to be a kind of Surface on which no Work is required in order for the Charge to travel from one place to another. With such Surfaces, they are the locus of all the points that lie on them. Thus, they have the same Potential. In order to move a charge, some work is required on almost all other types of Surfaces. That being said, it also does not hold true for Equipotential Surfaces. No, such Surfaces require absolutely zero Work in order for the Charge to move.