Question

Explain the concept of electric potential difference and electric potential.

Answer 1

A charge in an electric field possesses electric potential energy just as a particle in a gravitational field possesses gravitational potential energy. Consider a test charge q₀ in an electric field, moved very slowly by an external agent from point B where its electric potential energy is U_B to a point A where its electric potential energy is U_A.

The change in the potential energy, U_A– U_B is defined as the work W_B→A that must be done by an external agent to move the test charge from B to A against the electric force, keeping the charge always in equilibrium, i.-e., without accelerating the charge so as not to give it any kinetic energy.

W_B→A = ∆U = U_A – U_B

The potential difference ∆V = V_AB = V_A - V_B between two points A and B in electric field is ∆V = \(\cfrac{W_{B→A}}{q_0}\) = \(\cfrac{ΔU}{q_0}\)

Definition : The electric potential difference between two points in an electric field is defined as the work done per unit charge by an external agent against the electric force in moving an infinitesimal positive charge from one point to the other without acceleration.

We choose the potential energy U_B and potential V to be zero when the initial point B is infinitely far from the source charges which produce the field. Then, the work done per unit test charge by an external agent in bringing a test charge from infinity to a point is the electric potential at that point. The electric potential at a distance r from a source charge,

V(r) = \(\cfrac{W_{∞→r}}{q_0}\) = \(\cfrac{U(r)}{q_0}\)

Definition : The electric potential V at a point in an electric field is defined as the work per unit charge that must be done by an external agent against the electric force to move without acceleration a sufficiently small positive test charge from infinity to the point of interest.

[Note : It is more correct to speak about potential difference ∆V between two points than just the potential V at a given point because the latter implies a choice of .zero reference potential. The choice is one of convenience and we may choose the zero reference potential for a point at infinity or at some other location convenient for the problem as is done for gravitational potential.]