A thick metallic spherical shell of inner radius r1 and outer radius r2 has a charge +Q . A charge +q is placed at the centre of the shell. The charge per unit area on the outer surface is

Question

A thick metallic spherical shell of inner radius r1 and outer radius r2 has a charge +Q . A charge +q is placed at the centre of the shell. The charge per unit area on the outer surface is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/957650ee6f312aca6f7e32e1fb056cdf-.png" /> (A)  ((Q-q)/4π(r22 - r12))  (B)  ((Q-q)/4π r22 )  (C)  ((Q+q)/4π r22 )  (D)  ((Q+q)/4π (r22+r22) )

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/d3bce51c0dde5df109a03b266da3c695-.png" /> Charge on the outer surface = Q + q ∴ The charge per unit area = (Q +q/4 π r22)

Q. A thick metallic spherical shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge $+ Q$ . A charge $+ q$ is placed at the centre of the shell. The charge per unit area on the outer surface is

$\frac{( Q - q )}{4 π ( r _{2}^{2} - r _{1}^{2} )}$

$\frac{( Q - q )}{4 π r _{2}^{2}}$

$\frac{( Q + q )}{4 π r _{2}^{2}}$

$\frac{( Q + q )}{4 π ( r _{2}^{2} + r _{2}^{2} )}$

Charge on the outer surface $= Q + q$
$∴$ The charge per unit area $= \frac{Q + q}{4 π r _{2}^{2}}$

Q. A thick metallic spherical shell of inner radius r1​ and outer radius r2​ has a charge +Q . A charge +q is placed at the centre of the shell. The charge per unit area on the outer surface is

4π(r22​−r12​)(Q−q)​

4πr22​(Q−q)​

4πr22​(Q+q)​

4π(r22​+r22​)(Q+q)​