(a)
The magnitude of flux due to the current in the strip.
(a)
Answer to Problem 44E
The elemental flux through the strip is
Explanation of Solution
Write the expression for flux in the through strip.
Here,
Write the expression for the magnetic field in the strip.
Here,
Write the expression for the area of the strip.
Here,
Conclusion:
Substitute
Thus, the elemental flux through the strip is
(b)
The magnitude of the flux through the loop.
(b)
Answer to Problem 44E
The flux through the loop is
Explanation of Solution
Write the expression for the elemental flux through the strip in the loop.
Conclusion:
Integrate equation (2).
Here,
Solve the above integration.
Thus, the flux through the loop is
(c)
The magnitude of the induced EMF through the loop.
(c)
Answer to Problem 44E
The induced EMF through the loop is
Explanation of Solution
Write the expression for induced EMF.
Here,
Write the expression for the flux through the loop.
Conclusion:
Differentiate equation (4) with respect to
Here,
Substitute
Thus, the induced EMF through the loop is
(d)
The induced current in the loop.
(d)
Answer to Problem 44E
The induced current in the loop is
Explanation of Solution
Write the expression for induced EMF in the loop.
Write the expression for the induced current in the loop.
Here,
Conclusion:
Substitute
Thus, the induced current in the loop is
(e)
The direction of
(e)
Answer to Problem 44E
The direction of the induced current is clockwise.
Explanation of Solution
Write the expression for
Conclusion:
The induced current is proportional to the change in
Thus, the direction of the induced current is clockwise.
Want to see more full solutions like this?
Chapter 20 Solutions
General Physics, 2nd Edition
- In the circuit sho in the accompanying figure, the rtd slides along the conducting rails at a constant VelOCity v. The velocity is in the same plane as the rails and directed at an angle 6 to them. A uniform magnetic field Bis directed out of the page. What is the emf induced in the r?arrow_forwardThe armature and field coils of a series-wound motor have a total resistance of 3.0 . When connected to a 120-V source and running at normal speed, the motor draws 4.0 A. (a) How large is tire back emf? (b) What current will the motor draw just after it is turned on? Can you suggest a way to avoid this large initial current?arrow_forwardCheck Your Understanding (a) What is the magnetic flux through one turn of a solenoid of self- inductance 8.0 × 10-5 H when a current of 3.0 A flows through it? Assume that the solenoid has 1000 turns and is wound from wire of diameter 1.0 mm. (b) What is the cross-sectional area of the solenoid?arrow_forward
- 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_forwardIn an oscillating LC circuit the maximum charge on the capacitor is 2.0 × 10-6 C and the maximum current through the inductor is 8.0 mA. (a) What is the period of the oscillations? (b) How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged?arrow_forwardShow that Equation 32.28 in the text Ls Kirchhoffs loop rule as applied to the circuit in Figure P32.56 with the switch thrown to position b.arrow_forward
- Does the induced emf always act to decrease the magnetic flux through a circuit?arrow_forwardA rectangular wire loop with length a and width b lies in the xy-plane, as shownbelow. Within the loop there is a time-dependent magnetic field given by B(t)=C((xcost)i+(ysint)k) ,with B(t) intesla. Determine the emf induced in the loop as a function of time.arrow_forwardA single-turn circular loop of wire of radius 50 mm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.10-s time interval, the magnitude of the field Increases uniformly from 200 to 300 mT. (a) Determine the emf Induced in the ioop. (b) If the magnetic field is directed out of the page, what is the direction of the cun-ent induced in the loop?arrow_forward
- A steady current flows through a circuit with a large induct3ve time constant. When a switch in the circuit is opened, a large spark across the terminals of the switch. Explain.arrow_forwardA motor in normal operation carries a direct current of 0.850 A when connected to a 120-V power supply. The resistance of the motor windings is 11.8 . While in normal operation, (a) what is the back emf generated by the motor? (b) At what rate is internal energy produced in the windings? (c) What If? Suppose a malfunction slops the motor shaft from rotating. At what rate will internal energy be produced in the windings in this case? (Most motors have a thermal switch that will turn off the motor to prevent overheating when this stalling occurs.)arrow_forwardThe figure shows a rod of length L rod has resistance 0.459 ; the rest of the loop has negligible resistance. A current i 137A through the long straight wire at distance a = field throughout loop. Find the (a) magnitude of the emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod? 10.5 cm that is forced to move at constant speed v 5.60 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The 8.01 mm from the loop sets up a (nonuniform) magnetic X X X X X X XX X X x xx X Units (a) Number Units (b) Number Units (c) Number Units (d) Number Y Units Version 4.24.16.2 (e) Number 2000-2019 John Wiley & Sons, Inc. All Rights Reserved. A Division of John Wiley & Sons, Inc. ivacy Policy1arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill