(a) What is the maximum magnitude of the force on an aluminum rod with a 0.100-μC charge that you pass between the poles of a 1.50-T permanent magnet at a speed of 5.00 m/s?
(b) In what direction is the force?
Answer: (a) 7.5 x 10-7 N (b) perpendicular to both B and v (Click and drag over the answer to highlight it)
5.2
An oxygen-16 ion with a mass of 2.66 × 10−26 kg travels at 5.00 × 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
5.3
What Hall voltage is produced by a 0.200-T field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm/s?
Answer: 3.12 mV
5.4
(a) What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to the Earth’s 3.00×10−5-T field?
(b) What is the direction of the force if the current is straight up and the Earth’s field direction is due north, parallel to the ground?
Answer: (a) 0.6 N/m (b) West
5.5
A DC power line for a light-rail system carries 1000 A at an angle of 30.0º to Earth’s 5.00 × 10−5 T field.
(a) What is the force on a 100-m section of this line?
(b) Discuss practical concerns this presents, if any.
Answer: (a) 2.5 N
5.6
An AC appliance cord has its hot and neutral wires separated by 3.00 mm and carries a 5.00-A current.
(a) What is the maximum force per meter between the wires?
(b) Are the forces attractive or repulsive?
(c) Do appliance cords need any special design features to compensate for these forces?
Answer: (a) 1.7 mN/m (b) repulsive
5.7
(a) To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400-loop-per-meter circular coil 0.660 m in radius to create a 1.20-T field (typical of an MRI instrument) at its center with no iron present.
(b) The magnetic field of a proton is approximately like that of a circular current loop 0.650 × 10−15 m in radius carrying 1.05 × 104 A. What is the field at the center of such a loop?
Answer: (a) 3151 A (b) 1 x 1013 T
5.8
Calculate the size of the magnetic field 20 m below a high voltage power line. The line carries 450 MW at a voltage of 300,000 V.
Answer: 1.5 x 10-5 T
5.9
(a) What voltage will accelerate electrons to a speed of 6.00×106 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) 102 V (b) 2.9 mm (proton) and 68 µm (electron)
5.10
(a) What is the direction of the force on a wire carrying a current due east in a location where Earth’s field is due north? Both are parallel to the ground.
(b) Calculate the force per meter if the wire carries 20.0 A and the field strength is 3.00 × 10−5 T.
(c) What diameter copper wire would have its weight supported by this force?
(d) Calculate the resistance per meter and the voltage per meter needed.
Answer: (a) upward, perpendicular to the ground (b) 0.6 mN/m (c) 9.3 x 10-5 m (d) 2.45 Ω/m and 49 V/m
Physics Education Research at UNG 