Question

Three concentric spherical metallic shells $A,B,andC$ of radii $a,b,andc(a<b<c)$ have charge densities of $\sigma ,-\sigma and\sigma$ respectively. Match the column and select the correct answer using the codes given below
Codes :
P Q R S
(A)$2314$
(B)$1423$
(C)$4123$
(D)$2341$

Answer 1

Now charge on sphere of radius $a$ is $\sigma 4\pi a^2$

charge on sphere of radius b is $-\sigma 4\pi b^2$

charge on sphere of radius c is $\sigma 4\pi c^2$

potential on surface is given by $V=q/4\pi {ϵ}_{o}R$

Now for A $V_A=\sigma a/{ϵ}_o$

Similarly on surface of all sphere potential due to themselves is $\sigma /{ϵ}_o$

Now on surface of potential is due to sphere A ,B, and C

therefore, Therefore, $V_A=\text{potential due to (A+B+C) at (r=a) is}\sigma /{ϵ}_o(a-b+c)$

Similarly, since for sphere B $V_B=\text{potential due to (A+B+C) at (r=b) is}\sigma /{ϵ}_o(a^2/b-b+c)$

Now similarly for sphere C $V_C=\sigma {ϵ}_o(a^2/c-b^2/c+c)$

and field at surface of a is $\sigma /{ϵ}_o$