Write an expression for potential energy of two charges `q_(1) and q_(2) at vec(r_(1)) and vec(r_(2))` in a uniform electric field `vec(E)`.

Write an expression for potential at a point P vec(( r)) due to two point charges q_(1) and q_(2) at vec(r_(1)) and vec(r_(2)) respectivley.

Derive the expression for the potential energy of an electric dipole of dipole moment vec(p) placed in a uniform electric field vec(E ) .

Force vec(F) acting on a test charge q_(0) in a uniform electric field vec(E) is

Write the vector form of force acting between two charges q_1 and q_2 having vec r_1 and vec r_2 as their position vectors respectively.

Two point charges q_(1)andq_(2) are located at vec(r_(1))andvec(r_(2)) respectively in an external electric field E. Obtain the expression for the total work done in assembling this configuration.

A charge Q located at a point vec r is in equilibrium under the combined field of three charges q_(1), q_(2) and q_(3) . If the charges q_(1) and q_(2) are located at point vec r_(1) and vec r_(2) respectively, find the direction of the force on Q due to q_(3) in terms of q_(1),(q_2), vec r_(1) vec r_(2) , and vec(r) .

A charge Q located at a point vec r is in equilibrium under the combined field of three charges q_(1), q_(2) and q_(3) . If the charges q_(1) and q_(2) are located at point vec r_(1) and vec r_(2) respectively, find the direction of the force on Q due to q_(3) in terms of q_(1),(q_2), vec r_(1) vec r_(2) , and vec(r) .

(a) Write two properties by which electric potential is related to the electric field . (b) Two point charges q_(1) and q_(2) separated by a distance of r_(12) are kept in air. Derive an expression for the potential energy of the system of two charges .