First slide

Pontial due to

Question

Consider two concentric spherical metal shells of radii $r_{1}$ 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 :

Easy

A

$\frac{- r_{2}}{r_{1}} q$
B

zero
C

$\frac{- r_{1}}{r_{2}} q$
D

-q

Solution

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

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