Question

How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, relative to infinity, is 1.50 kV?

Answer 1

Answer:

$q=2.08*10^{-8}C\\ q=20.8nC$

Explanation:

Given data

Electric potential V=1.50 kV

Diameter d=25.0 cm

radius=diameter/2=25/2=12.5 cm=0.125 m

to find

We are asked to find excess charge

Solution

As inside the sphere the electric field is zero everywhere and potential is same at every point inside the sphere and on its surface

So we can use the value of the potential to get the charge q on the sphere

$V=\frac{1}{4\pi E}\frac{q}{R}\\ q=4\pi ERV\\Where\\4\pi E=\frac{1}{9.0*10^{9}N.m^{2}/C^{2} }\\ q=(\frac{1}{9.0*10^{9}N.m^{2}/C^{2} })(0.125m)(1.50*10^{3}V )\\q=2.08*10^{-8}C\\ q=20.8nC$