Consider two concentric spherical metal shells of radii r1 and r2 (r2 r1). If the outer shell has a charge q and the inner one is grounded, the charge on the inner shell is

Question

Consider two concentric spherical metal shells of radii r1 and r2 (r2 > r1). If the outer shell has a charge q and the inner one is grounded, the charge on the inner shell is (A) -(r2/r1)q (B) zero (C) -(r1/r2)q (D) -q

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ba95a285566fbfdee1acaf1fcac411b2-.png" /> Since the inner shell is grounded, therefore, its potential is zero. Let q' be charge on the inner shell. Then Vinner=(1/4πε0) ((q'/r1)+(q/r2))=0 or (q'/r1)+(q/r2)=0 or q' =-(r1/r2)q

Q. Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}$ $(r_{2} > r_{1})$ . If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is

$- \frac{r _{2}}{r _{1}} q$

zero

$- \frac{r _{1}}{r _{2}} q$

$- q$

Since the inner shell is grounded, therefore, its potential is zero. Let $q$ ' be charge on the inner shell. Then
$V_{inn er} = \frac{1}{4 π ε _{0}} (\frac{q ^{'}}{r _{1}} + \frac{q}{r _{2}}) = 0$
or $\frac{q ^{'}}{r _{1}} + \frac{q}{r _{2}} = 0$
or $q^{'} = - \frac{r _{1}}{r _{2}} q$

Q. Consider two concentric spherical metal shells of radii r1​ and r2​ (r2​>r1​). If the outer shell has a charge q and the inner one is grounded, the charge on the inner shell is

−r1​r2​​q