Chapter 20. Conceptual questions: 1,2,4,6,12,13 Quick Quizzes: 1,3,5 Problems: 26, 28, 34, 39,56. Induced Voltages and Inductance. Induced emf. A current can be produced by a changing magnetic flux. Magnetic Flux. A loop of wire is in a uniform magnetic field B The loop has an area A
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Conceptual questions: 1,2,4,6,12,13
Quick Quizzes: 1,3,5
Problems: 26, 28, 34, 39,56
Induced Voltages and Inductance
T m² = Wb (Weber)
The value of the magnetic flux is proportional to the total number of lines passing through the loop
For a single loop
For N tightly wound up loops
Since ΦB = B A cos θ, the change in the flux, ΔΦ, can be produced by a change in B, A or θ.
Thus, the induced electromotive force can be produced by changing B, A or θ, or their combinations.
The figure below is a graph of magnitude B versus time t for a magnetic field that passes through a fixed loop and is oriented perpendicular to the plane of the loop. Rank the magnitudes of the emf generated in the loop at the three instants indicated (a, b, c), from largest to smallest.
The induced, motional emf, acts like a battery in the circuit
You wish to move a rectangular loop of wire into a region of uniform magnetic field at a given speed so as to induce an emf in the loop. The plane of the loop must remain perpendicular to the magnetic field lines. In which orientation should you hold the loop while you move it into the region of magnetic field in order to generate the largest emf? (a) With the long dimension of the loop parallel to the velocity vector; (b) With the short dimension of the loop parallel to the velocity vector. (c) Either way—the emf is the same regardless of orientation.
What is the direction of the current induced in the resistor at the instant the switch is closed?
20-28. Find the direction of the current in R the instant the switch is closed.
ε = N B A ω sin ω t
Problem 20.34. A coil of area 0.10 m2 is rotating at 60 rev/s with its axis of rotation perpendicular to a 0.20-T magnetic field. (a) If there are 1 000 turns on the loop, what is the maximum voltage induced in the coil? (b) When the maximum induced voltage occurs, what is the orientation of the loop with respect to the magnetic field?
Using,emax = NBA w
=1000 (0.2T) (0.10m2) (120 p rad/s) = 7.5 103 V
Plane of the loop is parallel to the magnetic field
F = BA
[A is the cross-sectional area of the solenoid]
For a solenoid B = mon I = mo (N/l)I,
F = mo A NI/l
L = N F /I = mo A N2 /l
L depends only on geometric factors A and l, number of turns squared, and on mo
A solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. Find (a) its inductance and (b) the rate at which current must change through it to produce an emf of 75 mV.
The switch in the circuit shown in the figure below is closed and the lightbulb glows steadily. The inductor is a simple air-core solenoid. An iron rod is inserted into the interior of the solenoid, which increases the magnitude of the magnetic field in the solenoid. As the rod is inserted into the solenoid, the brightness of the lightbulb (a) increases, (b) decreases, or (c) remains the same.
13. If the current in an inductor is doubled, by what factor does the stored energy change?
A novel method of storing electrical energy has been proposed. A huge underground superconducting coil, 1.00 km in diameter, would be fabricated. It would carry a maximum current of 50.0 kA through each winding of a 150-turn Nb3Sn solenoid.
1. A heavy permanent magnet is moving toward a current carrying circular loop of wire. Which is correct?
A conducting bar is sliding at a constant velocity along two conducting horizontal rods. The rods are separated by a distance l and connected across by a resistor R. The entire apparatus is placed inside a magnetic field B directed into the page.
3. A conducting coil is rotated at a constant speed in an external magnetic field. Which of the following most likely represents the current generated within the coil as a function of time?