Question

Correct curve of potential $\left(V\right)$ versus distance $\left(r\right)$ from centre of two charged spherical shells is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

For given charged spherical shells

For $r<R:$

$V=\frac{kq}{R}-\frac{k\left(2q\right)}{2R}=0$

For $R<r<2R:$

$V=\frac{kq}{r}-\frac{k\left(2q\right)}{2R}$

$\Rightarrow V=\frac{kq}{r}-\frac{kq}{R}$
$=-ve[\text{for}r>R]$

Also, $V$ decreases as $r$ increases.

For $r>2R:$

$\Rightarrow V=\frac{kq}{r}-\frac{k\left(2q\right)}{r}=-ve$

With increase in $r$, $V$ decreases in magnitude as is evident from the graph.

Based on these observations, option $\left(a\right)$ is correct.

Why this question ? Concept- If $A\propto \frac{1}{B}$ then if $B$ is increases then $A$ will decrease. But if $A\propto \frac{-1}{B}$, then if $B$ is increases then $A$ will also increase as negative integer with less magnitude is greater.