A thick walled hollow spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. A charge q is placed at the centre of sphere. The surface charge densities on inner and outer surfaces of the sphere will be respectively

Question

A thick walled hollow spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. A charge q is placed at the centre of sphere. The surface charge densities on inner and outer surfaces of the sphere will be respectively (A) (-q/4π r21),(q/4π r22) (B) -(q/4π r21),(Q+q/4π r22) (C) -(q/4π r21),(Q-q/4π r22) (D) - (q/4π r21),(Q/4π r22)

Tardigrade Admin · Accepted Answer

By induction charge on inner surface is (-q) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/421d2f1c10338beb16c4310cd36f78ca-.png" /> σin=-(q/4π r21) σout = - (Q+q/4π R22)

Q. A thick walled hollow spherical conducting shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge Q. A charge q is placed at the centre of sphere. The surface charge densities on inner and outer surfaces of the sphere will be respectively

$\frac{- q}{4 π r _{1}^{2}}, \frac{q}{4 π r _{2}^{2}}$

$- \frac{q}{4 π r _{1}^{2}}, \frac{Q + q}{4 π r _{2}^{2}}$

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

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

By induction charge on inner surface is (-q)
$σ_{in} = - \frac{q}{4 π r _{1}^{2}}$
$σ_{o u t} = - \frac{Q + q}{4 π R _{2}^{2}}$

Q. A thick walled hollow spherical conducting shell of inner radius r1​ and outer radius r2​ has a charge Q. A charge q is placed at the centre of sphere. The surface charge densities on inner and outer surfaces of the sphere will be respectively

4πr12​−q​,4πr22​q​

−4πr12​q​,4πr22​Q+q​

−4πr12​q​,4πr22​Q−q​

−4πr12​q​,4πr22​Q​