Concepts Of Physics MCQ Edition [Volume 2]PhysicsGauss's Law
A charge Q is located at the centre of an initially uncharged, hollow metallic sphere of radius a . Determine the surface charge density on the inner surface and on the outer surface. If a charge q is subsequently placed on the sphere, what will be the surface charge densities on the inner and outer surfaces? Also, find the electric field inside the sphere at a distance x from the centre in both situations.
Options
- AInitial inner and outer densities: - Q 4 a^2 , Q 4 a^2 Final inner and outer densities: - Q 4 a^2 , Q+q 4 a^2
- BInitial inner and outer densities: 0 , Q 4 a^2 Final inner and outer densities: - Q 4 a^2 , q 4 a^2 Electric f
- CInitial inner and outer densities: Q 4 a^2 , - Q 4 a^2 Final inner and outer densities: Q 4 a^2 , q-Q 4 a^2 El
- DInitial inner and outer densities: - Q 4 a^2 , Q 4 a^2 Final inner and outer densities: 0 , Q+q 4 a^2 Electric
Correct answer
A. Initial inner and outer densities: - Q 4 a^2 , Q 4 a^2 Final inner and outer densities: - Q 4 a^2 , Q+q 4 a^2
Step-by-step solution
When a charge Q is placed at the centre of the uncharged hollow metallic sphere, the electric field inside the conducting material must be zero. By Gauss's law, a charge -Q is induced on the inner surface of the sphere. Since the sphere is initially uncharged, a charge +Q appears on the outer surface. Assuming the sphere is a thin shell of radius a , the surface charge density on the inner surface is - Q 4 a^2 and on the outer surface is Q 4 a^2 . When an additional charge q is given to the sphere, it resides entir