Page 3 - Lesson Note - 1

(d) Work done in moving a test charge from one point of equipotential surface to other is zero.

12. Relationship between electric field and potential gradient

where, negative sign indicates that the direction of electric field is from higher potential to lower
potential, i.e. in the direction of decreasing potential.
NOTE: (i) Electric field is in the direction of which the potential decreases steepest.
(ii) Its magnitude is given by the change in the magnitude of potential per unit displacement normal
to the equipotential surface at the point.
13. Electrostatic Potential Energy The work done against electrostatic force gets stored as
potential energy. This is called electrostatic potential energy.
∆U = U B-U A =W AB
14. The work done in moving a unit positive test charge over a closed path in an electric field is
zero. Thus, electrostatic forces are conservative in nature.
15. Electrostatic potential energy of a system of two point charges is given by

16. Electrostatic potential of a system of n point charges is given by

17. Potential Energy in an External Field
(i) Potential Energy of a single charge in external field Potential energy of a single charge q at a
point with position vector r, in an external field is qV(r),
where V(r) is the potential at the point due to external electric field E.
(ii) Potential Energy of a system of two charges in an external field

18. Potential energy of a dipole in a uniform electric field E is given by
Potential energy = -p .E
19. Electrostatic Shielding The process which involves the making of a region free from any
electric field is known as electrostatic shielding.