Three concentric spherical shells have radii a, b and c (a < b < c) anf have surface charge densities $$\sigma $$, $$-$$$$\sigma $$ and $$\sigma $$ respectively. If V_A, V_B and V_C denote the potentials of the three shells, then, for c = a + b, we have

The electric potential at a point (x, y, z) is given by V = $$-$$x²y $$-$$ xz³ + 4

The electric field at that point is

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

The electric potential at a point in free space due to charge Q coulomb is Q $$ \times $$ 10¹¹ volts. The electric field at that point is