Exam 29: Electromagnetic Induction

Electrons are circulating in a cyclotron in a uniform magnetic field of 1.1 T.One can think of these circulating electrons as a circular current loop with the same diameter.The magnetic field is then rapidly increased at a constant rate of 2.5 T/s.If the magnitude of the induced electric field causing the electrons to increase their speed 25 ms after the magnetic field begins increasing is 0.73 V/m,what is the diameter of the electrons' orbit? This is the basis for accelerating electrons in a betatron.

An elastic circular conducting loop expands at a constant rate in time.The radius is initially 0.200 m,but then begins to increase 0.018 m every second.The loop has a constant resistance of 15 $\varOmega$ and is placed in a region of uniform (same everywhere)magnetic field of 0.880 T,perpendicular to the plane of the loop.Calculate the magnitude of the induced current 2.4 s after the loop begins expanding.

What is the resistance of a series RL circuit in which L = 73 mH if the current increases to a quarter of its final value in 14 $\mu$ s?

A solenoid of cross sectional area 1.4 m² and n=300 turns/m carries a current of 4.0 A.It stores an energy of 3.4 J.What is the length of the solenoid?

A 9-V battery is connected through a switch to 2 identical resistors and an ideal inductor as shown in the figure.The 2 resistors each have a resistance of 20 ohms and the inductor has an inductance of 0.10 henries.The switch is initially open.Ten milliseconds after the switch is closed,what is the current in resistor R₂?

A metal loop has an area of 0.100 m² and is placed flat on the ground.There is a uniform magnetic field pointing due west.This magnetic field initially has a value of 0.123 T but this decreases to 0.075 T uniformly during a period of 0.579 s.Find the voltage induced in the loop during this time.

A popular demonstration of eddy currents is to drop a magnet down a long metal tube and a long glass or plastic tube.As the magnet falls down the tube there is changing flux as the magnet falls toward or away from each part of the tube.What tube has the larger voltage induced in it and what one has the larger current induced in it. V I

A circular wire loop of resistance 1.00 $\varOmega$ and diameter 5.0 cm rotates about a horizontal axis while in a region having a 0.10 T magnetic field pointing in a horizontal plane at an angle of 35 degrees relative to the rotation axis.If the maximum current induced in the loop is 6.7 mA,what is the period of the rotation?

A 1.0-m long straight wire is held in a horizontal east-west orientation and is then dropped.Supposing that the Earth's magnetic field at this location is 2.0 * 10^-5 T,due north,what will be the induced emf in the wire 2.0 s after it is released? (Hint: The wire is in free-fall,and you can thus calculate its velocity after the 2.0 s.)

The long straight wire in the figure has current I = 1 A flowing in it.A square loop which has 10-cm sides is positioned 10 cm away from the wire as shown.The loop is then moved in the positive x-direction with a speed v = 10 cm/s.If the loop has a resistance of 0.02 ohms,calculate the magnitude of the magnetic flux through the loop the instant the loop is made to move.

A circular coil of wire with 200 turns and a radius of 30 cm is laying flat on a horizontal wooden table.There is a uniform magnetic field at this location with a magnitude of 0.3 T that is directed to the north and down,making an angle of 25.8 ^$\circ$ with the horizontal.What is the magnitude of the magnetic flux through the coil?

Two conducting rails of negligible resistance terminate in a resistor of resistance R = 2.40 $\varOmega$ The rails are placed in a magnetic field B = 15.0 mT perpendicular to the plane of the rails.The magnetic field is uniform and time independent.The distance between the rails is w = 10.0 cm as shown in the figure.A conducting rod of negligible resistance slides frictionless on top of the two rails at a velocity v = 1.20 m/s + (3.4 m/s²)t,where t is the time,in seconds.The induced current in the circuit at t = 1.00 s is

A circular wire loop of resistance R = 1.0 $\varOmega$ rotates with period 150 ms about a horizontal axis while in a region having a 0.10 T magnetic field pointing in a horizontal plane at an angle of 35 degrees relative to the rotation axis.If the maximum current induced in the loop is 6.7 mA,what is the diameter of the loop?

A 1.1-H solenoid is fed by a direct current of 25A. Then the power source is disconnected.Then the two ends of the solenoid are directly connected by a wire.How many Joules of heat are produced if all of the energy that was stored goes into heating the wire?

A rod of length 3 cm moves perpendicular to a magnetic field with a velocity of 2.5 m/s,the magnetic field is 0.60 T.What is the induced voltage?

A 5-turn square loop (0.150 m along a side,resistance = 2.00 $\varOmega$ )is placed in a magnetic field that makes an angle of 30 ^$\circ$ with the normal to the plane of the loop.The magnitude of this field varies with time according to B = 2.40t⁴,where t is measured in s and B in T.What is the induced EMF in the coil at t = 1.38 s?

An elastic circular conducting loop expands at a constant rate in time.The radius is initially 0.200 m,but then begins to increase 0.018 m every second.The loop has a constant resistance of 15 $\varOmega$ and is placed in a region of uniform (same everywhere)magnetic field of 0.880 T,perpendicular to the plane of the loop.Calculate the magnitude of the induced EMF 2.4 s after the loop begins expanding.

A solenoid of radius 2 cm and length 15 cm has 120 turns.The rate of change of induced current through it to produce a self-induced emf of 4 mV is

A 2.0 m long solenoid of cross sectional area 1.4 m² and n=300 turns/m carries a current of 4.0 A.What is the energy density in the solenoid?

A solenoid with 100 turns and a cross sectional area of 20 cm² has a magnetic field of 0.60 T along its axis.If the field is confined within the solenoid and changes at a rate of 0.20 T/s,the magnitude of the induced EMF in the solenoid will be