Question

A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge`Q/2` is placed at its centre C and an other charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric flux through the shell.

Answer 1

(i) At point C, inside the shell

The electric field inside a spherical shell is zero thus, the force experienced by the charge at the centre of the shell C will also be zero.

`.:vec(F_C)=qvecE `

`.:vec(F_C)=0`

At point A,

`|vec(F_A)|=2Q(1/(4piepsilon_0)((3Q)/2)/x^2)`

`vecF_A=(3Q^2)/(4piepsilon_0x^2),`

(ii) Electric flux through the shell

`phi=1/epsilon_0xx" magnitude of the charge enclosed by the shell"`

`phi=1/epsilon_0xxQ/2=Q/(2epsilon_0)`