Question

Two metallic spheres of radii $a$ and $b$ are separated by a distance $d$ as shown in the figure. the capacity of the system is

• A. $\frac{4\pi {ϵ}_0}{\frac{1}{a}-\frac{1}{b}-\frac{2}{d}}$
  
• B. $\frac{4\pi {ϵ}_0}{\frac{1}{a}+\frac{1}{b}+\frac{2}{d}}$
  
• C. $\frac{4\pi {ϵ}_0}{\frac{1}{a}-\frac{1}{b}+\frac{2}{d}}$
  
• D. $\frac{4\pi {ϵ}_0}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$
  

Answer 1

The correct option is D $\frac{4\pi {ϵ}_0}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$



Potential on sphere I :

$V_1=\frac{Q}{4\pi {ϵ}_0}[\frac{1}{a}-\frac{1}{d}]$

Potential on sphere II :

$V_2=\frac{Q}{4\pi {ϵ}_0}[-\frac{1}{b}+\frac{1}{d}]$

$C=|\frac{Q}{\Delta V}|=\frac{4\pi {ϵ}_0}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$

Hence, option (d) is the correct answer.