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 another 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 the shell and at the point A,
(ii) the electric flux through the shell.
Doubt by Harshita
Solution :
(i) We know the electric field inside a charge spherical shell is always equals to zero (EC=0).
So, the force on the charge Q/2 at the centre of the shell will be given by
FC=charge × Electric field
FC=(Q/2)×EC
FC=(Q/2)×0
FC=0
Force Experienced by the charge at the point A (FA)
FA=(2Q)×EA
FA=(2Q)×[k(Q+Q/2)/r2]
FA=2Q×3kQ/2r2
FA=3kQ2/r2
ii) By Using Gauss's Theorem,
Electric Flux through the shell
ΦE=[Q/2]/ε₀
ΦE=Q/2ε₀
