Physics - Electrostatics Question with Solution | TestHub

Let the surface charge density is$\sigma .$

And,$q_A$and$q_B$are charges on shell$A$and$B$



$\therefore Q=q_A+q_B$

$or Q=4\pi r^2\sigma +4\pi R^2\sigma$

$\therefore \sigma =\frac{Q}{4\pi \left(r^2+R^2\right)}$

$\therefore V_C=V_A+V_B$

$\therefore V_C=\frac{q_A}{4\pi {ϵ}_{0}r}+\frac{q_B}{4\pi {ϵ}_{0}R}$

$=\frac{1}{4\pi {ϵ}_0} \left[\frac{q_A}{r}+\frac{q_B}{R}\right]=k \left(\frac{4\pi r^2\sigma }{r}+\frac{4\pi R^2\sigma }{R}\right)$

$=k \left(4\pi r\sigma +4\pi R\sigma \right)$

$=4\pi k \left[\frac{Qr}{4\pi \left(R^2+r^2\right)}+\frac{QR}{4\pi \left(r^2+R^2\right)}\right]$

$=\frac{kQ (R+r)}{(R^2+r^2)} \left(Here, k=\frac{1}{4\pi {ϵ}_0}\right)$