Suppose a 50-turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. The coil originally has an area of 0.250 m2. It is then compressed to have no area (A = 0) in 0.100 s. What is the direction and magnitude of the induced emf if the uniform magnetic field has a strength of 1.50 T?
Answer: clockwise, 188 V (Click and drag over the answer to highlight it)
6.2
An MRI technician moves her hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with her fingers pointing in the direction of the field.
(a) Find the average emf induced in her wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field.
(b) What current is induced in the ring if its resistance is 0.0100 Ω?
(c) What average power is dissipated?
(d) What magnetic field is induced at the center of the ring?
Answer: (a) 3 mV (b) 300 mA (c) 0.9 mW (d) 1.7 x 10-5 T
6.3
A 0.250 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.) Find the magnetic field strength needed to induce an average emf of 10,000 V.
Answer: 0.42 T
6.4
A lightning bolt produces a rapidly varying magnetic field. If the bolt strikes the earth vertically and acts like a current in a long straight wire, it will induce a voltage in a loop aligned like that in the figure.
(a) What voltage is induced in a 1.00 m diameter loop 50.0 m from a 2.00 × 106 A lightning strike, if the current falls to zero in 25.0 μs?
(b) Discuss circumstances under which such a voltage would produce noticeable consequences.
Answer: 251 V
6.5
A jet airplane with a 75.0 m wingspan is flying at 280 m/s.
(a) What emf is induced between wing tips if the vertical component of the Earth’s field is 3.00 × 10−5 T?
(b) Is an emf of this magnitude likely to have any consequences? Explain.
Answer: 0.63 V
6.6
At what angular velocity in rpm will the peak voltage of a generator be 480 V, if its 500-turn, 8.00 cm diameter coil rotates in a 0.250 T field?
Answer: 7300 rpm
6.7
A 75-turn, 10.0 cm diameter coil rotates at an angular velocity of 8.00 rad/s in a 1.25 T field, starting with the plane of the coil parallel to the field.
(a) What is the peak emf?
(b) At what time is the peak emf first reached?
(c) At what time is the emf first at its most negative?
(d) What is the period of the AC voltage output?
Answer: (a) 5.9 V (b) 0.2 s (c) 0.59 s (d) 0.79 s
6.8
A plug-in transformer supplies 9.00 V to a video game system.
(a) How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 400 turns?
(b) What is its input current when its output is 1.30 A?
Answer: (a) 30 (b) 0.098 A
6.9
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
(a) What is the ratio of turns in the primary and secondary coils of her transformer?
(b) What is the ratio of input to output current?
(c) How could a New Zealander traveling in the United States use this same transformer to power her 240 V appliances from 120 V?
Answer: (a) Vp/Vs = 2 (b) Ip/Is = 0.5
6.10
The plug-in transformer for a laptop computer puts out 7.50 V and can supply a maximum current of 2.00 A.
(a) What is the maximum input current if the input voltage is 240 V? Assume 100% efficiency.
(b) If the actual efficiency is less than 100%, would the input current need to be greater or smaller? Explain.
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