1) A thin rod extends along the z-axis from z = -d to z = d. The rod carries a charge Q uniformly distributed along its length 2d with linear charge density λ = Q / 2d. Find the electric potential at a point z > d along the z-axis. Indicate clearly where you have chosen your zero reference point for your potential.
Use the result that E = - ∇V to find the electric field at a point z > d along the z-axis.
Can you obtain an expression for the electric potential or electric field when z < d?
2) A thin washer of outer radius b and inner radius has a uniform negative surface charge density - σ on the washer (note that σ > 0).
a) If we set V (∞) = 0, what is the electric potential difference between a point at the center of the washer and infinity, V (0) - V (∞)?
b) An electron of mass m and charge q = -e is released with an initial speed vo from the center of the hole (at the origin) in the upward direction (along the perpendicular axis to the washer) experiencing no forces except repulsion by the charges on the washer. What speed does it ultimately obtain when it is very far away from the washer (i.e. at infinity?)
c) If a positron of charge +e was released a small distance from the center of the hole, along the perpendicular axis to the washer, what might be its fate?
3) An electron is initially accelerated between two plates, with a voltage difference of 300 V between them. It then passes through a hole in a screen into a region where there is a uniform electric field of 900 N/C. If the velocity of the electron is in the same direction as this field, then how far will the electron move before it reverses its direction? What was the maximum speed attained by the electron?
4) Convert a kilowatt hour (kWh) into electron volts (eV).
5) A circular wire loop of 10 turns exists in a plane and has a radius of 1 cm. This wire loop is placed in a solenoid such that the plane of the loop is at 60° to the axis of the solenoid. The solenoid has 100 turns per meter, a radius of 2 cm and a current which varies from 2 A to 1 A in 1 s. Find the emf in the wire loop.
6) A helicopter blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade. This rotation occurs in a region where the component of the earth's magnetic field perpendicular to the blade is 30 µT. If the blade is 60 cm in length, what is the magnitude of the potential difference between its ends?