10 questions

13 minutes

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1. Each of the resistors shown in the circuit below has a resistance of 200 Ω. The emf of the ideal battery is 24 V.

What is the ratio of the power dissipated by R_{1} to the power dissipated by R_{4}?

2. What is the value of the following product?

20 μF × 500 Ω

3.

A copper wire in the shape of a circle of radius 1 m, lying in the plane of the page, is immersed in a magnetic field, B, that points into the plane of the page. The strength of B varies with time, t, according to the equation

B(t) = 2t(1 – t)

where B is given in teslas when t is measured in seconds. What is the magnitude of the induced electric field in the wire at time t = 1 s?

4.

In the figure above, the top half of a rectangular loop of wire, x meters by y meters, hangs vertically in a uniform magnetic field, B. Describe the magnitude and direction of the current in the loop necessary for the magnetic force to balance the weight of the mass m supported by the loop.

5.

A solid nonconducting cylinder of radius R and length L contains a volume charge density given by the equation ρ(r) = (+3 C/m^{4})r, where r is the radial distance from the cylinder's central axis. This means that the total charge contained within a concentric cylinder of radius r < R and length 这是啥 < L is equal to 2π这是啥r^{3}. Find an expression for the strength of the electric field inside this cylinder.

6.

The figure above shows a pair of long, straight current-carrying wires and four marked points. At which of these points is the net magnetic field zero?

7.

The figure above shows two positively charged particles. The +Q charge is fixed in position, and the +q charge is brought close to +Q and released from rest. Which of the following graphs best depicts the acceleration of the +q charge as a function of its distance r from +Q?

8.

Once the switch S in the figure above is closed and electrostatic equilibrium is regained, how much charge will be stored on the positive plate of the 6 μF capacitor?

9.

A metal bar of length L is pulled with velocity v through a uniform magnetic field, B, as shown above. What is the voltage produced between the ends of the bar?

10. An electric dipole consists of a pair of equal but opposite point charges of magnitude 4.0 nC separated by a distance of 2.0 cm. What is the electric field strength at the point midway between the charges?