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  1. How much excess charge must be placed on a copper sphere25.0cmin diameter so that the potential of its centre, relative to infinity, is3.75kV?
  2. What is the potential of the sphere’s surface relative to infinity?

Short Answer

Expert verified
  1. The charge should be 52.0nC.
  2. The potential of the sphere’s surface relative to infinity is 3.75kV.

Step by step solution

01

Formula for the potential

In the sphere that has charge q and radius R, the potential can be calculated as:

V=14πεoqR

Where q is the charge and R is the radius of a sphere

02

Determine the charge

(a)

Inside the sphere, the electric field is zero everywhere, and the potential is the same at every point inside the sphere and on its surface. So, the potential can be used to get the charge.

V=14πεoqR

q=4πεoRV

Plug the values in the above expression, and we get,

q=19.0×1090.1253.75×103=52.0nC

Thus, the charge should be 52.0nC.

03

Determine the potential

(b)

As explained in part (a), the potential is constant inside the sphere, on the surface of the sphere, and inside it, so the potential at the surface relative to infinity is 3.75kV.

Thus, the potential of the sphere’s surface relative to infinity is 3.75kV.

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