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 σ 1 is the surface charge on the inner surface and Q1 net charge on it and σ 2 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 σ 1 is the surface charge on the inner surface and Q1 net charge on it and σ 2 the surface charge on the outer surface and Q2 net charge on it then: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-dzww5mltiah9.png" /> (A) σ 1=0, Q1=0 , σ 2=0, Q2=0 (B) σ 1≠ 0, Q1=0 , σ 2≠ 0, Q2=0 (C) σ 1≠ 0,Q1≠ 0 , σ 2≠ 0, Q2≠ 0 (D) σ1=0, Q1=0 σ2=0, Q2=0

Tardigrade Admin · Accepted Answer

Net charge inside the cavity is zero. ∴ Q1=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

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

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

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

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

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

σ1​=0,Q1​=0 , σ2​=0,Q2​=0

σ1​=0,Q1​=0 , σ2​=0,Q2​=0

σ1​=0,Q1​=0 , σ2​=0,Q2​=0

σ1​=0,Q1​=0σ2​=0,Q2​=0

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

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

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

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

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

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