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# Three Charged Spheres

Let's discuss a problem where we will find the charge of the sphere with the help of the three charged spheres problem. Try before reading the solution.

The Problem:

Consider three concentric metallic spheres $A$, $B$ and $C$ of radii of $a$, $b$, $c$ respectively where a<b<c . $A$ and $B$ are connected whereas C is grounded The potential of the middle sphere $B$ is raised to $V$ then what is the charge on the sphere $C$?

Solution:

Three concentric metallic spheres $A$, $B$ and $C$ have radii of $a$, $b$, $c$ respectively where a<b<c . $A$ and $B$ are connected whereas C is grounded The potential of the middle sphere $B$ is raised to $V$.

$$V=\frac{Kq}{b}+\frac{KQ}{c}$$ $$\Rightarrow \frac{k(q+Q)}{c}=0$$
$$\Rightarrow q+Q=0$$
$$\Rightarrow q=-Q$$
$$\frac{k(-Q)}{b}+\frac{KQ}{c}=V$$
$$\Rightarrow KQ(\frac{1}{c}-\frac{1}{b})=V$$
$$Q=\frac{bcV}{(b-c)}4\pi\epsilon_0$$

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