AL AKHAWAYN UNIVERSITY School of Science and Engineering

Final Exam –Summer 2001 (PHY1402)

Date: July 17, 2001 Instructor: Dr. H. Darhmaoui Duration: 110 min. Place: Building 7, Room 02 1. An RL circuit has a 60 V battery, a 30 H inductor, a 12 Ω resistor, and a switch S,

in series as shown in Figure 1. Initially the switch is open, and there is no magnetic flux in the inductor. At time t = 0 s, the switch is closed.

(a) What is the current in the circuit at t = 3.5 s? (b) At what time the inductor voltage is 24 V? (c) What is the current in the circuit when the resistor

voltage is equal to the inductor voltage? (d) At what time the magnetic energy of the inductor

is equal to half its terminal value?

2. A rectangular current loop is carrying current I1 = 7.0 A, in the direction shown in

Figure 2, is located near a long wire carrying a current Iw. The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire. If the net force on the loop is to have magnitude 4.6 10-6 N and is directed towards the wire, what must be the magnitude and direction of the current Iw in the wire?

3. A solenoid is wound with 400 turns on a form of 4.0 cm in diameter and 50 cm long.

The windings carry a current in the sense that is shown in Figure 3-(a). The current produces a magnetic field, of magnitude 1.5 mT, at the center of the solenoid. (assume B is constant inside the solenoid)

(a) What is the current in the solenoid windings? (b) What is the magnetic flux in the solenoid? (c) A view of the solenoid, showing clockwise sense of the current in the windings, is

given in Figure 3-(b). An electron is in circular motion near the center of the solenoid, with an orbital diameter of 3.0 cm. What is the speed of the electron and the direction of the orbital motion?

4. A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 2.0 A, as shown in Figure 4. A uniform external magnetic field of magnitude 1.2 T in the negative x-direction is present. Segment CD is in the x-z plane and forms a 25° angle with the z-axis, as shown.

(a) What is the y-component of the magnetic force on segment AB? (b) An external torque applied to the loop keeps it in static equilibrium. What is its

magnitude? (c) What is the magnetic flux of the external field through the loop?

5. Three point charges are placed at the following (x, y) coordinates: charge 7.0 10-6 C at (0,0.60m), charge 9.0 10-6 C at (0.8m,0), and charge –4.0 10-6 C at (0.80m, 0.60m).

(a) Calculate the electric field and electric potential at the origin (0,0) due to these three charges. (Take the zero potential to be at infinity).

(b) What is the electric potential energy of the system. 6. A heating element of resistance (at its operating temperature) 185 Ω is connected

to a battery of emf 144 V and unknown internal resistance r. It is found that heat energy is being generated in the heater element at a rate of 80 W. What is the rate at which heat energy is being generated in the internal resistance of the battery?

7. A rectangle 10.0 cm x 20.0 cm is placed so that its right edge is 40.0 cm to the left

of a mirror. Draw the image seen through the mirror and calculate the area of the image if

a. The mirror is plane as in Figure 5-a. b. The mirror is concave as in Figure 5-b (the radius of curvature of the

mirror is 20.0 cm) 20.0 cm 40.0 cm 20.0 cm

40.0 cm

10.0 cm

10.0 cm

Figure 5-a Figure 5-b 8. Two thin converging lenses of focal lengths f1 = 10.0 cm and f2 = 20.0 cm are

separated by 20.0 cm, as in Figure 6. An object is placed 15.0 cm to the left of the first lens. Find:

a. The position of the final image relative to the object. b. The magnification of the system.

f1 = 10.0 cm f2 = 20.0 cm

Figure 6

15.0 cm

20.0 cm

9. In the circuit shown in Figure 7, the generator delivers five times as much current at very low frequencies than it delivers at high frequencies. Find the ratio R2/R1 of the resistances.

10. A series RLC circuit (Figure 8) has a 50 Hz ac source, a 30 Ω resistor, a 0.20 H inductor, and an 80 µF capacitor. The rms current in the circuit is 2.5 A.

a. Find the voltage amlitude of the source, the power factor of the circuit and the rms voltage across points a and b in the circuit.

b. The frequency of the source is changed so that the capacitive reactance is equal to twice the inductive reactance. The original circuit elements are retained. What is the new frequency of the source?

c. Now the capacitance is changed so that the circuit is in resonance. The original resistor and inductor are retained. The voltage and the frequency of the source are kept at the original values. What is the new capacitance?

Figure 8