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1) The potential at the surface of a 15cm radius sphere is 5.0kV What is the cha

ID: 2289606 • Letter: 1

Question

1) The potential at the surface of a 15cm radius sphere is 5.0kV

What is the charge on the sphere, assuming it's distributed in a spherically symmetric way?

2)You're developing a switch for high-voltage power lines. The smallest part in your design is a 6.0cm diameter metal sphere.

What do you specify for the maximum potential on your switch if the electric field at the sphere's surface isn't to exceed the 3 MV/m breakdown field of air?

3)The electric potential in a region is given by V=-Vo r/R, where Vo and R are constants, r is the radial distance from the origin, and the zero of potential is taken at r=0.

Find the magnitude of the electric field in this region.

and find the direct of the electric field in this region. Is it inward or outward?

Explanation / Answer

"Determine the magnitude of the electric field in the region r<a."
From Gauss' Law:
E(4?r^2) = +Q/?o
E = +Q/[(4??o)r^2]

"Determine the magnitude of the electric field in the region a<r<b"
The electric field inside of a conductor (with no current) is zero.

"Determine the magnitude of the electric field in the region r>b."
Again, from Gauss' Law:
E(4?r^2) = +3Q/?o
E = +3Q/[(4??o)r^2]

"How much charge is on the inside surface of the hollow sphere?"
For the electric field in the region a<r<b to be zero, the charge on this surface would be equal in magnitude, but opposite in sign to the point charge in the center: -Q.

"How much charge is on the exterior surface?"
If the conductor has a total charge of +2Q and the charge on the inner surface is -Q, the charge on the outside surface would be: +2Q - (-Q) = +3Q