PHYS 2212 Module 8 Self Assessment Practice Problems

Module 8 Self Assessment Practice Problems

8.1
A pair of point charges, q = +7.50 µC and q’= -5.00 µC, are moving as shown in the figure with speeds v = 9.00 x 104 m/s and v’ = 6.00 x 104 m/s. The charges are at the locations shown in the figure.
(a) What is the magnitude of the magnetic field produced at the origin?
(b) What is the direction of the magnetic field produced at the origin?
Answer:  (a) 9.4 x 10-7 T  (b) into the page
8.2
What is the magnetic field at P due to the current I in the wire shown?
Answer: 
8.3
An electron is moving in the vicinity of a long, straight wire that lies along the x axis. The wire has a constant current of 8.00 A in the -x direction. At an instant when the electron is at point (0, 0.200 m, 0), the electron’s velocity is .
(a) What are the x, y, and z components of the force that the wire exerts on the electron?
(b) Calculate the magnitude of this force.
Answer:   (a) -3.84 x 10-20 N, -6.4 x 10-20 N, 0   (b) 7.46 x 10-20 N
8.4
Two long, straight wires, one above the other, are separated by a distance 2a and are parallel to the x axis. Let the +y axis be in the plane of the wires in the direction from the lower wire to the upper wire. Each wire carries current I in the +x direction. Find  — the net magnetic field of the two wires at the following points in the plane of the wires. (Express your answer in terms of the variables I, a, and appropriate constants µ0 and π.)
(a) Midway between the wires.
(b) At a distance a above the upper wire.
(c) At a distance a below the lower wire.
Answer: (a) 0 (b) (c)
8.5
An electric bus operates by drawing current from two parallel overhead cables, at a potential difference of 600 V, and spaced 57 cm apart. The power input to the bus’s motor is at its maximum power of 65 hp (1 hp = 745.7 W).
(a) What current does it draw?
(b) What is the repulsive force per unit length between the cables?
Answer:  (a) 80.8 A  (b) 0.0023 N/m
8.6
Two long, parallel wires are hung by cords of length 5.0 cm, as shown in the accompanying figure. Each wire has a mass per unit length of 30 g/m, and they carry the same current in opposite directions. What is the current if the cords hang at 6.0° with respect to the vertical?
Answer:  40 A
8.7
Long, straight conductors with square cross section, each carrying current I, are laid side-by-side to form an infinite current sheet with current directed out of the plane of the page. A second infinite current sheet is a distance d below the first and is parallel to it. The second sheet carries current into the plane of the page. Each sheet has n conductors per unit length.
(a) Calculate the magnitude and direction of the net magnetic field at point P (above the upper sheet). Express your answer in terms of the variables I, d, n, and appropriate constants.
(b) Calculate the magnitude and direction of the net magnetic field at point R (midway between the two sheets). Express your answer in terms of the variables I, d, n,  and appropriate constants.
(c) Calculate the magnitude and direction of the net magnetic field at point S (below the lower sheet). Express your answer in terms of the variables I, d, n, and appropriate constants.
Answer: (a) 0  (b) µ0nI  (c) 0
8.8
A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c in the following figure. The central conductor and tube carry equal currents I in opposite directions. The currents are distributed uniformly over the cross sections of each conductor.
(a) Derive an expression for the magnitude of the magnetic field at points outside the central, solid conductor but inside the tube (a < r < b). Express your answer in terms of the variables I, r, and µ0.
(b) Derive an expression for the magnitude of the magnetic field at points outside the tube (r > c). Express your answer in terms of the variables I, r, and µ0.
Answer: (a) µ0I/2πr (b) 0
8.9
A solenoid that is 34.0 cm long and contains 440 circular coils 1.40 cm in diameter carries a 1.80 A current.
(a) What is the magnetic field at the center of the solenoid, 0.700 cm from the coils?
(b) Suppose we now stretch out the coils to make a very long wire carrying the same current as before. What is the magnetic field 0.700 cm from the wire?
(c) Is the magnetic found in part (b) the same as you found in part (a)? Why or why not?
Answer:    (a) 2.9 mT  (b) 51 µT
8.10
A magnetic field of 37.2 T has been achieved at the MIT Francis Bitter National Magnetic Laboratory. Find the current needed to achieve such a field…
(a) 2.2 cm from a long, straight wire
(b) at the center of a circular coil of radius 42 cm that has 100 turns
(c) near the center of a solenoid with radius 2.6 cm, length 30 cm, and 40,000 turns.
Answer:   (a) 4.1 x 106 A   (b) 2.5 x 105 A   (c) 222 A