Concept explainers
(a)
The magnitude of the induced current in the wire.
(a)
Answer to Problem 31.20P
The magnitude of the induced current in the wire is
Explanation of Solution
Given info: The radius of the upper circle is
Write the expression for the area of the loop.
Here,
For upper circle.
Substitute
Thus, the area of the upper circle is
For lower circle.
Substitute
Thus, the area of the lower circle is
Write the expression for the magnetic flux through a coil
Here,
Write the expression for the emf of the coil.
Here,
Substitute
For the upper circle.
Substitute
Thus, the emf induced in the upper loop is
For the lower circle.
Substitute
Thus, the emf induced in the upper loop is
Write the expression for the resistance.
Here,
For upper circle.
Substitute
Thus, the resistance in the upper circle is
For lower circle.
Substitute
Thus, the resistance in the lower circle is
Write the expression for the induced current.
Substitute
Conclusion:
Therefore, the magnitude of the induced current in the wire is
(b)
The direction of the induced current in the wire.
(b)
Answer to Problem 31.20P
The current is clockwise in the upper loop and the current is counterclockwise in the lower loop
Explanation of Solution
Given info: The radius of the upper circle is
Write the expression for the induced current in the wire.
Consider negative current as clockwise and positive current as counterclockwise.
From the above expression, the induced current is directly proportional to the induced emf. From part (a), the value of the induced emf for upper loop is negative, so the value of the current is also negative. The negative current shows the current is clockwise in the upper loop. And also from part (a), the value of the induced emf for lower loop is positive, so the value of the current is also positive. The positive current shows the current is counterclockwise in the lower loop. Thus, the current is clockwise in the upper loop and the current is counterclockwise in the lower loop.
Conclusion:
Therefore, the current is clockwise in the upper loop and the current is counterclockwise in the lower loop.
Want to see more full solutions like this?
Chapter 31 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- Within the green dashed circle show in Figure P30.21, the magnetic field changes with time according to the expression B = 2.00t3 4.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.50 cm. When t = 2.00 s, calculate (a) the magnitude and (b) the direction of the force exerted on an electron located at point P, which is at a distance r = 5.00 cm from the center of the circular field region. (c) At what instant is this force equal to zero? Figure P30.21arrow_forwardWhy is the following situation impossible? A conducting rectangular loop of mass M = 0.100 kg, resistance R = 1.00 , and dimensions w = 50.0 cm by = 90.0 cm is held with its lower edge just above a region with a uniform magnetic field of magnitude B = 1.00 T as shown in Figure P30.34. The loop is released from rest. Just as the top edge of the loop reaches the region containing the field, the loop moves with a speed 4.00 m/s. Figure P30.34arrow_forwardDesign a current loop that, when rotated in a uniform magnetic field of strength 0.10 T, will produce an emf =0 sin t. where 0=110V and 0=110V .arrow_forward
- A wire is bent in the form of a square loop with sides of length L (Fig. P30.24). If a steady current I flows in the loop, determine the magnitude of the magnetic field at point P in the center of the square. FIGURE P30.24arrow_forwardThe conducting rod shown in the accompanying figure moves along parallel metal rails that are 25-cm apart. The system is in a uniform magnetic field of strength 0.75 T, which is directed into the page. The resistances of the rod and the rails are negligible, but the section PQ has a resistance of 0.25 . (a) What is the emf (including its sense) induced in the rod when it is moving to tire right with a speed of 5.0 m/s? (b) What force is required to keep the rod moving at this speed? (c) What is the rate at which work is done by this force? (d) What is the power dissipated in the resistor?arrow_forwardTwo frictionless conducting rails separated by l = 55.0 cm are connected through a 2.00- resistor, and the circuit is completed by a bar that is free to slide on the rails (Fig. P32.71). A uniform magnetic field of 5.00 T directed out of the page permeates the region, a. What is the magnitude of the force Fp that must be applied so that the bar moves with a constant speed of 1.25 m/s to the right? b. What is the rate at which energy is dissipated through the 2.00- resistor in the circuit?arrow_forward
- A square loop whose sides are 6.0-cm long is made with copper wire of radius 1.0 mm. If a magnetic field perpendicular to the loop is changing at a rate of 5.0 mT/s, what is the current in the loop?arrow_forwardHow many turns must be wound on a flat, circular coil of radius 20 cm in order to produce a magnetic field of magnitude 4.0105 T at the center of the coil when the current through it is 0.85 A?arrow_forwardThe accompanying figure shows a cross-section of a long, hollow, cylindrical conductor of inner radius r1= 3.0 cm and outer radius r2= 5.0 cm. A 50-A current distributed uniformly over the cross-section flows into the page. Calculate the magnetic field at r = 2.0 cm. r = 4.0 cm. and r = 6.0 cm.arrow_forward
- A conducting single-turn circular loop with a total resistance of 5.00 is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by B = a + bt2 ct3, where a = 4.00 Wb, b = 11.0 Wb/s2, and c = 6.00 Wb/s3. B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 3.50 s?arrow_forwardA circular coil 15.0 cm in radius and composed of 145 tightly wound turns carries a current of 2.50 A in the counterclockwise direction, where the plane of the coil makes an angle of 15.0 with the y axis (Fig. P30.73). The coil is free to rotate about the z axis and is placed in a region with a uniform magnetic field given by B=1.35jT. a. What is the magnitude of the magnetic torque on the coil? b. In what direction will the coil rotate? FIGURE P30.73arrow_forwardThe homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical contact) at its axle and another at a point on its circumference as shown in Figure P23.21. A uniform magnetic field is applied perpendicular to the plane of the disk. Assume the field is 0.900 T, the angular speed is 3.20 103 rev/min, and the radius of the disk is 0.400 m. Find the emf generated between the brushes. When superconducting coils are used to produce a large magnetic field, a homopolar generator can have a power output of several megawatts. Such a generator is useful, for example, in purifying metals by electrolysis. If a voltage is applied to the output terminals of the generator, it runs in reverse as a homopolar motor capable of providing great torque, useful in ship propulsion.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning