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Electricity problems

1. Two spherical drops of mercury each have a charge of 0.1 nC and a potential of 300v at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

2. A long thin straight wire with linear charge density (lambda) runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has a net linear charge density (2 * lambda) . Assume (lambda) is positive. Find expressions for the electric field strength.

A) Inside the cylinder (r<R)
B) Outside the Cylinder (r>R)

In what direction the electric field points in each case?

3. A hollow metal sphere has inner radius "a" and outer radius "b". Hollow sphere has charge + 2Q. A point charge + Q sits at the centre of the hollow sphere.

a) Determine the electric fields in the three regions r<= a, a<r<b and r>= b.

b) How much charge is on the inside surface of the hollow sphere and outside surface?

4. The conducting charge in the attached figure has been given an excess negative charge. The surface density of excess electrons at the center of the top surface is 5 * 10^10 electrons / m^2.

What are the electric field strengths E1 to E3 at points 1 to 3?