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# Electricity problems

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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?

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## Electricity & Magnetism Qualitative Problems

Here is a list of Qualitative problems which need the physics explained for each, diagrams, and equations with text are welcome.

1) The vector potential and the magnetic field inside and outside of a diamagnetic sphere in a uniform magnetic field

2) The vector potential and the magnetic field inside and outside of a uniformly magnetized sphere

3) Sketch the vector potential for at least four simple geometric cases, explain the sketches.

4) The electric potential and the electric field for (charge) monopoles, dipoles and quadrupoles

5) The vector potential and the magnetic field for (magnetic) monopoles, dipoles and quadrupoles

6) Surface polarization charges (aka, bound surface charges) versus volume polarization charges (aka, bound volume charges)

7) Surface magnetization currents (aka, bound surface currents) versus volume magnetization currents (aka, bound volume currents)

8) The relationship between the magnetic scalar potential and the magnetic field

9) The electric potential and the electric field inside capacitors containing dielectrics

10) The electric potential and the electric field inside capacitors containing ferroelectrics

11) The vector potential and the magnetic field inside inductors containing diamagnets

12) The vector potential and the magnetic field inside inductors containing ferromagnets

13) The displacement current and Maxwell's equations

14) E for a charge inside a dielectric; B for a point magnetic dipole inside a diamagnet

15) P for changing electric fields; M for changing magnetic fields

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