Question

Three conducting spheres A, B and C are a s shown in the figure. The radii of the spheres are a, b and c respectively. A and B are connected by a conducting wire. The capacity of the the system is then

• A. $4\pi {\epsilon }_0(a+b+c)$
• B. $4\pi {\epsilon }_0\left(\frac{bc}{c-d}\right)$
• C. $4\pi {\epsilon }_0[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}]$
• D. $4\pi {\epsilon }_0\left[\frac{abc}{ab+bc+ca}\right]$

Answer 1

The correct option is B $4\pi {\epsilon }_0\left(\frac{bc}{c-d}\right)$

Given, the sphere B and A are connected the system is equivalent to two sphere- with only sphere C of radius C.

$C=4\pi E_0\left[\frac{bc}{c-b}\right]$