Shown in the figure are two point charges + Q and — Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ1 is the surface charge on the inner surface and Q1 net charge on it and σ2 the surface charge on the outer surface and Q2 net charge on it then :

Question

Shown in the figure are two point charges + Q and — Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ1 is the surface charge on the inner surface and Q1 net charge on it and σ2 the surface charge on the outer surface and Q2 net charge on it then : (A) σ1 ≠ 0, Q1 ≠ 0; σ2 ≠ 0, Q2 ≠ 0 (B) σ1 ≠ 0, Q1 = 0; σ2 ≠ 0, Q2 = 0 (C) σ1 ≠ 0, Q1 = 0; σ2 = 0, Q2 = 0 (D) σ1 = 0, Q1 = 0; σ2 = 0, Q2 = 0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/81d8c8a5bd716eb42762c7b7e8a3c1d8-.png" /> Net charge inside the cavity is zero. Net charge inside the cavity is zero. ∴ Q 1=0 text and σ1=0 There is no effect of +Q,-Q and induced charge on inner surface on the outer surface hence Q 2=0, σ2=0

$σ_{1} \neq = 0, Q_{1} \neq = 0; σ_{2} \neq = 0, Q_{2} \neq = 0$

$σ_{1} \neq = 0, Q_{1} = 0; σ_{2} \neq = 0, Q_{2} = 0$

$σ_{1} \neq = 0, Q_{1} = 0; σ_{2} = 0, Q_{2} = 0$

$σ_{1} = 0, Q_{1} = 0; σ_{2} = 0, Q_{2} = 0$

Net charge inside the cavity is zero.
Net charge inside the cavity is zero.
$< b r / > ∴ Q_{1} = 0 and σ_{1} = 0 < b r / >$
There is no effect of $+ Q, - Q$ and induced charge on inner surface on the outer surface hence
$< b r / > Q_{2} = 0, σ_{2} = 0 < b r / >$

σ1​=0,Q1​=0;σ2​=0,Q2​=0

σ1​=0,Q1​=0;σ2​=0,Q2​=0

σ1​=0,Q1​=0;σ2​=0,Q2​=0

σ1​=0,Q1​=0;σ2​=0,Q2​=0

Net charge inside the cavity is zero. Net charge inside the cavity is zero. <br/>∴Q1​=0 and σ1​=0<br/> There is no effect of +Q,−Q and induced charge on inner surface on the outer surface hence <br/>Q2​=0,σ2​=0<br/>

$σ_{1} \neq = 0, Q_{1} \neq = 0; σ_{2} \neq = 0, Q_{2} \neq = 0$

$σ_{1} \neq = 0, Q_{1} = 0; σ_{2} \neq = 0, Q_{2} = 0$

$σ_{1} \neq = 0, Q_{1} = 0; σ_{2} = 0, Q_{2} = 0$

$σ_{1} = 0, Q_{1} = 0; σ_{2} = 0, Q_{2} = 0$

Net charge inside the cavity is zero.
Net charge inside the cavity is zero.
$< b r / > ∴ Q_{1} = 0 and σ_{1} = 0 < b r / >$
There is no effect of $+ Q, - Q$ and induced charge on inner surface on the outer surface hence
$< b r / > Q_{2} = 0, σ_{2} = 0 < b r / >$