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Charges on Conductors

Inside a neut...

Question

Inside a neutral metallic spherical shell, a charge $Q_{1}$ is placed, and outside the shell, a charge $Q_{2}$ is placed.

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Solution

Electric field due to any point charge is $E = k \frac{q}{r^{2}}$ . So it is depend on the charge and distance.

A) As charge $Q_{1}$ is placed at center so field inside the shell is remains non zero. i.e, $E = k \frac{Q_{1}}{r^{2}} \neq 0$ .

Thus, $A \to 2$

B) charge $Q_{1}$ is not at center but total charge remains same inside the shell will be same. So field inside the shell is remains non zero. i.e, $E = k \frac{Q_{1}}{r^{2}} \neq 0$ . Thus, $B \to 2$

C) As position of $Q_{1}$ is changed so field inside will be changed but non zero.

$C \to 2, 3$

D) similarly when position of $Q_{2}$ is changed ,filed inside remains non zero but field outside will change. thus , $D \to 2, 4$

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Column- $I$	Column- $II$
$(i) .$ If $q_{1}$ is at center and $q_{2} = 0$ , then $\to E$ at center of shell due to charge on outer surface of shell is	$(a) . \frac{q_{1}}{4 π ε_{0} r^{2}}$
$(ii) .$ If $q_{1}$ is at center and $q_{2}$ is at distance $r$ from the center, then $\to E$ at a point distant $r_{2}$ ( $> r$ ) from the center of the shell due to outer surface charge is	$(b) .$ Zero
$(iii) .$ If $q_{1}$ is not at center and $q_{2} = 0$ , then $\to E$ at point $P$ ( $P$ is at distance $r$ from $q_{1}$ due to charge of the inner surface of shell) is	$(c) .$ Cant be determined

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