PHYS 2212 Module 7 Self Assessment Practice Problems

Module 7 Self Assessment Practice Problems

7.1
Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a 0.500 µC charge and flies due west at a speed of 660 m/s over Earth’s south magnetic pole, where the 8.00 x 10-5 T magnetic field points straight down into the ground.
(a) What are the direction and the magnitude of the magnetic force on the plane?
(b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.
Answer:  2.64 x 10-8 N South
7.2
An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of 6.64 x 10-27 kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.80-T magnetic field.
(a) What is the diameter of the path followed by this alpha particle?
(b) What effect does the magnetic field have on the speed of the particle? Explain why.
(c) What is the magnitude of the acceleration of the alpha particle while it is in the magnetic field?
(d) What is the direction of this acceleration?
Answer:   (a) 0.82 mm   (b) no effect   (c) 3.1 x 1012 m/s2   (d) horizontal, perpendicular to v
7.3
An oxygen-16 ion with a mass of 2.66 x 10-26 kg travels at 5.0 x 106 m/s perpendicular to a 1.20 T magnetic field, which makes it move in a circular arc with a 0.231 m radius.
(a) What positive charge is on the ion?
(b) What is the ratio of this charge to the charge of an electron?
(c) Discuss why the ratio found in (b) should be an integer.
Answer: (a) 4.8 x 10-19 C   (b) 3
7.4
(a)  What voltage will accelerate electrons to a speed of 6.00 x 107 m/s?
(b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated through the same potential.
Answer:  (a) 10.2 kV   (b) rproton = 43relectron
7.5
(a) What is the speed of a beam of electrons when the simultaneous influence of an electric field of 1.56 x 104 V/m and a magnetic field of 4.62 x 10-3 T, with both fields normal to the beam and to each other, produces no deflection of the electrons?
(b) When the electric field is removed, what is the radius of the electron orbit?
(c) What is the period of the orbit?
Answer:    (a) 3.38 x 106 m/s   (b) 4.16 mm   (c) 7.73 ns
7.6
The circuit shown in the figure is used to make a magnetic balance to weigh objects. The mass m to be measured is hung from the center of the bar, that is in a uniform magnetic field of 1.50 T, directed into the plane of the figure. The battery voltage can be adjusted to vary the current in the circuit. The horizontal bar is 60.0 cm long and is made of extremely light-weight material. It is connected to the battery by thin vertical wires that can support no appreciable tension; all the weight of the suspended mass m is supported by the magnetic force on the bar. A resistor with R = 5.00 Ω is in series with the bar; the resistance of the rest of the circuit is much less than this.
(a) Which point, a or b, should be the positive terminal of the battery?
(b) If the maximum terminal voltage of the battery is 175 V, what is the greatest mass m that this instrument can measure?
Answer:   (a) a   (b) 3.2 kg
7.7
A 2.60-N metal bar, 0.850 m long and having a resistance of 10.0 Ω, rests horizontally on conducting wires connecting it to the circuit shown. The bar is in a uniform, horizontal, 1.60-T magnetic field and is not attached to the wires in the circuit. What is the acceleration of the bar just after the switch S is closed?
Answer: 10.3 m/s2 
7.8
The plane of a rectangular loop of wire with a width of 5.0 cm and a height of 8.0 cm is parallel to a magnetic field of magnitude 0.18 T. The loop carries a current of 7.0 A.
(a) What torque acts on the loop?
(b) What is the magnetic moment of the loop?
(c) What is the maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field?
Answer:  (a) 0.005 N•m   (b) 0.028 A•m2   (c) 0.0068 N•m
7.9
In the Bohr model of the hydrogen atom, in the lowest energy state the electron orbits the proton at a speed of 2.2 x 106 m/s in a circular orbit of radius 5.3 x 10-11 m.
(a) What is the orbital period of the electron?
(b) If the orbiting electron is considered to be a current loop, what is the current I?
(c) What is the magnetic moment of the atom due to the motion of the electron?
Answer:  (a) 1.5 x 10-16 s  (b) 1.1 mA   (c) 9.3 x 10-24 A•m2
7.10
A coil with a magnetic moment of 1.46 A•m2 is oriented initially with its magnetic moment antiparallel to a uniform magnetic field of magnitude 0.810 T. What is the change in potential energy of the coil when it is rotated 180° so that its magnetic moment is parallel to the field?
Answer:  -2.37 J