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

Let, the charge on the inner shell be q' The total charge will be zero So, (k q'/r1)+(k q/r2)=0 (∵ r2 > r1) ⇒ q'=-(K q / r2/K / r1) 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

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

$- q$

Let, the charge on the inner shell be $q^{^{'}}$
The total charge will be zero
So, $\frac{k q ^{^{'}}}{r _{1}} + \frac{k q}{r _{2}} = 0 (∵ r_{2} > r_{1})$
$\Rightarrow q^{^{'}} = - \frac{K q / r _{2}}{K / r _{1}}$
$q^{^{'}} = - (\frac{r _{1}}{r _{2}}) q$

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