Two concentric hollow spheres are arranged as shown in the figure. If a charge +Q is given to the outer sphere, find charge induced on the inner sphere.

A spherical conducting shell of inner radius r_1 and outer radius r_2 has a charge Q as shown in the figure. A charge q is placed at the centre of the shell. What is the surface charge density of the inner and outer sufaces of the shell?

A charge q is distributed over two concentric hollow spheres of raddii r and R such that the surface densities are equal. Find the potential at the common centre.

A conductor A with cavity as shown in the figure a charge Q. Show that the entire charge must appear on the outer surface of the conductor.

Two small charged metal sphere A and B are situated in a vaccum. The distance between the centres of the spheres is 12.0 cm, as shown in the fig. The charge on each sphere may be assumed to be a point charge at the centre of the sphere. Point P is a movable point that lies on the line joining the centres of the sphere and is distance x fromt he centre of sphere A. The variation with distance x fo the electric field strength E at point P as shown in the figure. State the evidence provided by in the fig for the statement that the spheres are conductors, the charges on the spheres are either both positive or both negative.

S_1 and S_2 are two parallel concentric spheres enclosing charges Q and 2Q respectively as shown in the figure. How will the electric flux through the sphere S_1 change, if a medium of dielectric constant 5 is introduced in the space inside S_1 in plae at air?

Two small charged metal sphere A and B are situated in a vaccum. The distance between the centres of the spheres is 12.0 cm, as shown in the fig. The charge on each sphere may be assumed to be a point charge at the centre of the sphere. Point P is a movable point that lies on the line joining the centres of the sphere and is distance x fromt he centre of sphere A. The variation with distance x fo the electric field strength E at point P as shown in the figure. Use fig to state and explain the distance x at which the rate of change of potential with distance is maximum and minimum.

A spherical capacitor has an outer sphere of radius 0.15m and the inner sphere of diameter 0.2m The outer sphere is earthed and the inner shere is given charge of 6 muC. The space between the concentric spheres is filled with a material of dielectric constant 6. Calculate capacitacne and potential of inner sphere.

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be v. If the shell is now given a charge of -3 Q, the new potential difference between the same two surfaces is _____.

A point charge +Q is placed at the centre O of an uncharged hollow spherical conductor of inner radius 'a' and outer radius 'b'. Find the following: The magnitude and sign of the charge induced on the inner and outer surface of the conducting shell.