PHYS 2212 Module 9 Self Assessment Practice Problems

Module 9 Self Assessment Practice Problems

9.1
A single loop of wire with an area of 0.0940 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.140 T/s.
(a) What emf is induced in this loop?
(b) If the loop has a resistance of 0.650 Ω, find the current induced in the loop.
Answer:    (a) 13 mV  (b) 20 mA
9.2
A square loop whose sides are 6.0-cm long is made with copper wire of radius 1.0 mm. If a magnetic field perpendicular to the loop is changing at a rate of 5.0 mT/s, what is the current in the loop?
Answer: 13.8 mA
9.3
The rod shown below moves to the right on essentially zero-resistance rails at a speed of v = 3.0 m/s. If B = 0.75 T everywhere in the region, what is the current through the 5.0-Ω resistor? Does the current circulate clockwise or counterclockwise?
Answer: 18 mA, clockwise
9.4
A circular loop of wire with a radius of 15.0 cm and oriented in the horizontal xy-plane is located in a region of uniform magnetic field. A field of 1.6 T is directed along the positive z-direction, which is upward. If the loop is removed from the field region in a time interval of 2.7 ms, find the average emf that will be induced in the wire loop during the extraction process.
Answer: 41.9 V
9.5
A coil with 3.80 cm radius, containing 600 turns, is placed in a uniform magnetic field that varies with time according to B = (1.20 x 10-2 T/s)t + (3.40 x 10-5 T/s4)t4. The coil is connected to a 540-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.
(a) Find the magnitude of the induced emf in the coil as a function of time.
(b) What is the current in the resistor at time t0 = 4.50 s?
Answer: (a) |ε(t)| = 32.7 mV + (0.37 mV/s3)t3  (b) 0.123 mA
9.6
A circular loop of wire with radius 0.0440 m and resistance 0.168 Ω is in a region of spatially uniform magnetic field, as shown in the following figure. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.39 T and is decreasing at a rate of -0.698 T/s.
(a) Is the induced current in the loop clockwise or counterclockwise? Explain.
(b) What is the rate at which electrical energy is being dissipated by the resistance of the loop? 
Answer:  (a) counterclockwise  (b) 0.11 mW
9.7
A long, thin solenoid has 900 turns per meter and radius 2.50 cm. The current in the solenoid is increasing at a uniform rate of 42.0 A/s.
(a) What is the magnitude of the induced electric field at a point near the center of the solenoid?
(b) What is the magnitude of the induced electric field at a point 0.500 cm from the axis of the solenoid?
(c) What is the magnitude of the induced electric field at a point 1.00 cm from the axis of the solenoid?
Answer:  (a) 0  (b) 1.19 x 10-4 V/m  (c) 2.38 x 10-4 V/m
9.8
A circular loop of wire of radius 10 cm is mounted on a vertical shaft and rotated at a frequency of 5 cycles per second in a region of uniform magnetic field of 0.2 mT perpendicular to the axis of rotation.
(a) Find an expression for the time-dependent magnetic flux through the ring.
(b) Determine the time-dependent current through the ring if it has a resistance of 10 Ω.
Answer:  (a) Φ(t) = (6.28 x 10-6 Wb)cos(31.4t)  (b) I(t) = (1.97 x 10-5 A)sin(31.4t)
9.9
A coil with 50 turns and area 10 cm2 is oriented with its plane perpendicular to a 0.75-T magnetic field. If the coil is flipped over (rotated through 180°) in 0.20 s, what is the average emf induced in it?
Answer: 0.38 V
9.10
A metal ring 4.50 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.250 T/s.
(a) What is the magnitude of the electric field induced in the ring?
(b) In which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?
Answer:   (a) 2.8 mV/m  (b) counterclockwise