Question

A total electric charge of 3.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 24.0 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sphere: (a) 48.0 cm; (b) 24.0 cm; (c) 12.0 cm

Answer 1

Answer:

a, V = 65.6V

b. V = 131.0V

C. V = 131.0V

Explanation:

Given

Total electric charge $q= 3.50nC=3.50\times10^{-9}C$ distributed  uniform at surface of metal sphere where radius is R = 24cm

R = 24cm = 0.024m

we have to find potential at different distance

a. r = 48cm = 0.048m

b. r = 24cm = 0.024m

c. r = 12cm = 0.012m

a. solution

Here the distance r is grater then R,we can get the potential outside of sphere

$V = \dfrac{q}{4\pi\varepsilon_0r}$

$\textrm{where is} \dfrac{1}{4\pi\varepsilon_0}=9.0\times10^{9}N.m^{2}/c^2$

now we plug the value q and r in potential v

$V=(9\times10^9N.m^2/C^2)\dfrac{3.50\times10^{-9}C}{0.48m}$

=65.6V

b.solution

Here distane r is the same from radius R, so we can get potential inside sphere

$v= \dfrac{q}{4\pi\varepsilon_0R}$

Now we plug the value of R and q

$V=(9\times10^9N.m^2/C^2)\dfrac{3.50\times10^{-9}C}{0.24m}$

$V=131V$

3.solution

Inside sphere electric feild is zero.so potential is the same every point inside sphere and equal potential on the surface

$V=131V$