INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

September 15, 2017

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 \(V\).

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

Useful links:

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com