The difference between the two rotations and check whether they are indistinguishable.
Answer to Problem 62PQ
When the coil is parallel to the field and is rotated to a position where it is perpendicular to the field, the emf induced is found to be negative. The emf is found to be positive, when the coil is rotated back to its initial position. Both the rotations are distinguishable.
Explanation of Solution
Faraday’s law states that, when the magnetic flux changes an emf is induced in the coil.
The direction of the induced emf is given by Lenz law. Lenz law states that the change in flux is opposed by the current induced in the circuit due to a change in magnetic field. The current induced in the circuit, exerts a mechanical force as well.
Write the expression for induced emf from Faraday’s and Lenz law.
Here,
Write the expression for magnetic flux.
Here,
Write the expression for magnitude of the vector
Here,
Write the expression for magnitude of the magnetic flux.
Here,
Write the expression for initial flux linked with the coil.
Here,
Substitute
Write the expression for final flux linked with the coil.
Here,
Substitute
Substitute
Write the equation for change in magnetic flux.
The coil is now rotated back to its initial position. The coil now rotates from the position where the magnetic flux linked with it is
Therefore,
Write the expression for induced emf due to second rotation.
Conclusion:
Substitute
Substitute
Substitute
Therefore, the current in the coil flows in the counter clockwise direction.
Substitute
The induced current flows in the clockwise direction.
Therefore, when the coil is parallel to the field and is rotated to a position where it is perpendicular to the field, the emf induced is found to be negative. The emf is found to be positive, when the coil is rotated back to its initial position. Both the rotations are distinguishable.
Want to see more full solutions like this?
Chapter 32 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A metal bar of length 25 cm is placed perpendicular to a uniform magnetic field of strength 3 T. (a) Determine the induced emf between the ends of the rod when it is not moving, (b) Determine the emf when the rod is moving perpendicular to its Length and magnetic field with a speed of 50 cm/s.arrow_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_forwardA flat, square coil of 20 turns that has sides of length 15.0 cm is rotating in a magnetic field of strength 0.050 T. If tlie maximum emf produced in die coil is 30.0 mV, what is the angular velocity of the coil?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_forwardThe square armature coil of an alternating current generator has 200 turns and is 20.0 cm on side. When it rotates at 3600 rpm, its peak output voltage is 120 V. (a) Wliat is the frequency' of the output voltage? (b) What is the strength of the magnetic field in which the coil is turning?arrow_forwardReview. Figure P31.31 shows a bar of mass m = 0.200 kg that can slide without friction on a pair of rails separated by a distance = 1.20 m and located on an inclined plane that makes an angle = 25.0 with respect to the ground. The resistance of the resistor is R = 1.00 and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails?arrow_forward
- A rectangular conducting loop with dimensions w = 32.0 cm and h = 78.0 cm is placed a distance a = 5.00 cm from a long, straight wire carrying current I = 7.00 A in the downward direction (Fig. P32.75). a. What is the magnitude of the magnetic flux through the loop? b. If the current in the wire is increased linearly from 7.00 A to 15.0 A in 0.230 s, what is the magnitude of the induced emf in the loop? c. What is the direction of the current that is induced in the loop during this time interval?arrow_forwardA square, flat loop of wire is pulled at constant velocity through a region of uniform magnetic field directed perpendicular to the plane of the loop as shown in Figure OQ23.9. Which of the following statements are correct? More than one statement may be correct. (a) Current is induced in the loop in the clockwise direction. (b) Current is induced in the loop in the counterclockwise direction. (c) No current is induced in the loop. (d) Charge separation occurs in the loop, with the top edge positive. (e) Charge separation occurs in the loop, with the top edge negative.arrow_forwardA stiff spring with a spring constant of 1200.0 N/m is connected to a bar on a slide generator as shown in Figure P32.40. Assume the bar has length l = 60.0 cm and mass m = 0.75 kg, and it slides without friction. The bar connects to a U-shaped wire to form a loop that has width w = 40.0 cm and total resistance 25 and that sits in a uniform magnetic field B = 0.35 T. The bar is initially pulled 5.0 cm to the left and released so that it begins to oscillate. What is the induced current in the loop as a function of time, I(t)? (Ignore any effects due to the magnetic force on the oscillating bar.)arrow_forward
- The bar in Figure OQ23.10 moves on rails to the right with a velocity v, and a uniform, constant magnetic field is directed out of the page. Which of the following statements are correct? More than one statement may be correct. (a) The induced current in the loop is zero. (b) The induced current in the loop is clockwise. (c) The induced current in the loop is counterclockwise. (d) An external force is required to keep the bar moving at constant speed. (e) No force is required to keep the bar moving at constant speed.arrow_forwardA thin conducting bar (60.0 cm long) aligned in the positive y direction is moving with velocity v=(1.25m/s)i in a region with a spatially uniform 0.400-T magnetic field directed at an angle of 36.0 above the xy plane. a. What is the magnitude of the emf induced along the length of the moving bar? b. Which end of the bar is positively charged?arrow_forwardA square loop with side length L, mass M, and resistance R lies in the xy plane. A magnetic field B = B0(y/L) k is present in the region of the space near the loop. Determine the magnitude and direction of the induced current in the loop as the loop starts moving at velocity v = B0(y/L) j.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 Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning