A material with resistivity ρ is formed into a cylinder of length L and outer radius R. A cylindrical core with radius r is removed from the axis of this cylinder and filled with a conducting material, which is attached to a wire. The outer surface of the cylinder is coated with a conducting material and attached to another wire.
A) If the second wire has potential V greater than the first wire, in what direction does the local electric field point inside of the cylinder?
B) The magnitude of this electric field is c/r, where c is a constant and r is the distance from the axis of the cylinder. Use the relationship V = ∫E→⋅dl→ to determine the constant c.
C) What is the equation for the resistance of this device in terms of V, L, ρ , R and r ?
D) A 1.00 cm-long hollow cylindrical resistor has an inner radius of 1.50 mm and an outer radius of 3.00 mm. The material is a blend of powdered carbon and ceramic whose resistivity ρ may be altered by changing the amount of carbon. If this device should have a resistance of 6.80 kΩkΩ, what value of ρ should be selected?
