Answer to Question #133151 in Mechanics | Relativity for Shaik Abbas Ali

Question

Two Spheres of radius 6cms, having charges 10^-8C, -3×10^-8C. Find the potential of 2 spheres and potential at midpoint of centres if the distance between centres is 2m.

Answer 1

$q_1=10^{-8}C ;q_2=-3\times 10^{-8}C ;r_1=r_2=6\ cm$ $=0.06 \ m$

Potential at the surface of first sphere$=\frac{kq_1}{r_1}=\frac{9\times 10^9\times 10^{-8}}{0.06}=1.5\times 10^3 N/m$

Potential at the surface of first sphere$=\frac{kq_2}{r_2}=\frac{9\times 10^9\times (-3)\times 10^{-8}}{0.06}=-4.5\times 10^3 N/m$

Distance between their centers$=\ 2\ m$

So,distance of mid point from center of each sphere$=d_1=d_2=1\ m$

Potential at the mid point due to first sphere$=\frac{kq_1}{d_1}=\frac{9\times 10^9\times 10^{-8}}{1}=90 N/m$

Potential at the mid point due to second sphere$=\frac{kq_2}{d_2}=\frac{9\times 10^9\times (-3)\times 10^{-8}}{1}=-270 N/m$

Net potential at the mid point will be $=(90+(-270)) N/m=-180 \ N/m$