(a)
The maximum induced emf in the coil.
(a)
Answer to Problem 31.71AP
The maximum induced emf in the coil is
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The area of the rectangular coil is,
Here,
Substitute
Thus, the area of the coil is
The angle between the normal area component and the magnetic field is,
Here,
The flux induced in the coil is,
Here,
The emf induced in the coil is,
Substitute
Substitute
The induced emf is maximum for the maximum value of
Substitute
Substitute
Conclusion:
Therefore, the maximum induced emf in the coil is
(b)
The maximum rate of change of magnetic flux.
(b)
Answer to Problem 31.71AP
The maximum rate of change of magnetic flux is
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The induced flux is,
Substitute
Differentiate the above equation with respect to time with respect to time for the rate of change of flux.
For the maximum rate of change of flux the value of
Substitute
Substitute
Conclusion:
Therefore, the maximum rate of change of magnetic flux is
(c)
The induced emf at
(c)
Answer to Problem 31.71AP
The induced emf at
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The expression for the induced emf is,
Substitute
Conclusion:
Therefore, the induced emf at
(d)
The torque exerted by magnetic field on the coil for maximum emf.
(d)
Answer to Problem 31.71AP
The torque exerted by magnetic field on the coil is
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The formula to calculate the induced current in the coil is,
Here,
Substitute
Thus, the current in the coil is
The formula to calculate the magnetic moment of the coil is,
The formula to calculate the torque experienced by the coil is,
The maximum value of
Substitute
Substitute
Substitute
Conclusion:
Therefore, the torque exerted by magnetic field on the coil is
Want to see more full solutions like this?
Chapter 31 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- A 5000-pF capacitor is charged to 100 V and then quickly connected to an 80-mH inductor. Determine (a) the maximum energy stored in the magnetic field of the inductor, (b) the peak value of the current, and (c) the frequency of oscillation of the circuit.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_forwardSuppose that a rectangular toroid has 2000 windings and a self-inductance of 0.040 H. If h = 0.10 m, what is the current flowing through a rectangular toroid when the energy in its magnetic field is 2.0 × 10-6 J?arrow_forward
- A 50-turn coil has a diameter of 15 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.50 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil if the magnetic field is reduced to zero uniformly in (a) 0.10 s, (b) 1.0 s, and (c) 60 s.arrow_forwardA coil with a self-inductance of 3.0 H carries a current that decreases at a uniform rate dl/dt = -0.050 A/s. What is the emf induced in the coil? Describe the polarity of the induced emf.arrow_forwardA long solenoid of radius a with n turns per unit length is carrying a tune-dependent current I(t)=I0sintwhere I0 and are constants. The solenoid is surrounded by a wire of resistance R that has two circular loops of radius b with b>a. Find the magnitude and direction of current induced m the outer loops at tune t=0.arrow_forward
- A 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_forwardA long, cylindrical solenoid with 100 turns per centimeter has a radius of 1.5 cm. (a) Neglecting end effects, that is the self-inductance per unit length of the solenoid? (b) If the current through the solenoid changes at the rate 5.0 AJs, what is the emf induced per unit length?arrow_forwardThe current in a 62 mH inductor changes with time as I = bt- at. With a = 6 A/s and b = the magnitude of the induced emf, E, at 6 A/s, find t = 0.7 s. Answer in units of V. At what time is the emf zero?arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning