Q 12-02-106JEE MainJEE Main 2023 (10 Apr, Shift 1)Medium
Three concentric spherical metallic shells $X$, $Y$ and $Z$ of radius $a$, $b$ and $c$ respectively ($a<b<c$) have surface charge densities $\sigma$, $-\sigma$ and $\sigma$, respectively. The shells $X$ and $Z$ are at same potential. If the radii of $X$ and $Y$ are $2$ cm and $3$ cm, respectively, the radius of shell $Z$ is ______ cm.
Numerical value type. Enter your answer.
Answer: 5
With $Q=4\pi r^2\sigma$:
$$V_X=\frac{\sigma}{\epsilon_0}(a-b+c),\qquad V_Z=\frac{\sigma}{\epsilon_0}\left(\frac{a^2-b^2}{c}+c\right)$$
Equating: $a-b=\dfrac{(a-b)(a+b)}{c}\Rightarrow c=a+b=5$ cm.
Solution by Sreeraj P, M.Sc Physics