an electric current creates a magnetic field•a magnetic field exerts a force on a moving charged particle•

In this chapter we continue our study of the connections between electricity and magnetism. In the previous chapter (Chapter 21) we learned that

In this chapter we learn that a changing magnetic field creates ("induces") an electric field. (More accurately, a changing magnetic flux creates ("induces") an electric field. We'll learn about magnetic flux later in this chapter.) If a wire is nearby, the induced electric field causes a current to flow in the wire. Thus, a changing magnetic field induces a current in a conductor. This is the main process that we use to produce electricity on a mass scale.

Note that the textbook speaks of an induced emf, Ɛ; remember that emf is a potential difference ("voltage difference"), which provides an alternative, equivalent description of an electric field E. Remember that the induced emf and the induced electric field are distinct representations of the same phenomenon; they have different units, and are different quantities, so don't confuse them.

Chapter 22 Electromagnetic InductionWednesday, March 24, 2010 3:16 PM

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Example: A uniform magnetic field of magnitude 0.73 T is parallel to the axis of a circular loop of wire of radius 8.5 cm. (That is, the loop has radius 8.5 cm, not the wire!)(a) Determine the induced emf in the wire if the magnetic field is suddenly (i.e., in 0.01 s) turned off.(b) Determine the current in the wire if the wire's resistance is 0.062 Ω.

Solution: (a) Use Faraday's law of induction.

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(b) Using Ohm's law, we obtain

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Problem: Magnetic resonance imaging (MRI) is a medical technique for producing "pictures" of the interior of the body. The patient is placed within a strong magnetic field. One safety concern is what would happen to the positively and negatively charged particles in the body fluids if an equipment failure caused the magnetic field to be shut off suddenly. An induced emf could cause these particles to flow, producing an electric current within the body. Suppose the largest surface of the body through which flux passes has an area of 0.032 m2 and a normal that is parallel to a magnetic field of 1.5 T. Determine the smallest time period during which the field can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V.

Solution: Use Faraday's law of induction.

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Problem: The magnetic flux that passes through one turn of a 12-turn coil of wire changes to 4.0 Wb from 9.0 Wb in a time of 0.050 s. The average induced current in the coil is 230 A. What is the resistance of the wire?

Solution: Use Faraday's law of induction to determine the induced emf, then use Ohm's law to determine the resistance of the wire.

This is a large enough time to be of serious concern. The MRI operators must be careful not to abruptly shut the power off, and power failures must be avoided. To keep things safe, the magnet should be turned off over a time period of at least 10 s or so, as one always builds in a safety cushion.

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Bicycle generator (for a headlight)

Geothermal Power Generator

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Hydroelectric power generator

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Transformers

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Problem: The adaptor for my laptop converts 120 V AC to 19 V AC, and then to 19 V DC. We won't bother with the AC to DC conversion, which is beyond the scope of this course; just focus on the step-down AC transformation.(a) Determine the ratio of the number of turns in the primary and secondary coils of the transformer.(b) Determine the ratio of the currents in the primary and secondary coils.

Solution:

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Solution:

Thus, for example, if N2 is 100, then N1 is 630.

The current is higher in the secondary coil, by a factor of 6.3.

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Problem: (a) Determine the resistance of a 150-km-long aluminum cable that has a cross-sectional area of 8 square centimetres.

Your generating station produces 1500 MW of electric power and you decide to transmit it along the cable of Part (a). Determine the resistive power loss if the power is transmitted at (b) 250 kV and 6 kA.(c) 750 kV and 2 kA.

Solution: (a) The resistivity of aluminum is

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Thus, the resistance of the cable is

As a percentage of the generated power, the power loss is

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Transformers provided a powerful tool with which George Westinghouse (aided especially by Nikola Tesla, and his numerous amazing inventions involving AC motors, generators, and other AC electrical devices) won the "War of Currents" against Thomas Edison. Tesla designed the Niagara Falls, NY electric power generating station, among many other achievements.

Below is a photograph of a statue of Tesla in Queen Victoria Park in Niagara Falls, ON.

Conclusion: Transmitting power with higher voltages and lower currents decreases power losses. But this requires transforming generated power to high voltages and then transforming back down to lower voltages for use in homes and industries. This makes AC power very practical, as transformers use AC current.

(This calculation is OK in broad outline, but it's incorrect in detail because AC current tends to be transmitted near the skin of the cable, and so the resistance calculation needs to be modified. You can deal with this in your second-year electronics courses!)________________________________________________________

As a percentage of the generated power, the power loss is

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Problems and Solutions:

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One of the significant problems with electrical power generation is that it must be generated just when it is used. Sure, we can store electrical energy using batteries, but the capacities of available batteries is quite low. Battery technology is an active area of research, and if someone could figure out an efficient way to store large quantities of electrical energy this would be a terrific advance.______________________________________________________

Problem: A 10-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.20 Ω. Pulling the wire with a force of 1.0 N causes 4.0 W of power to be dissipated in the circuit. (a) Determine the speed of the wire. (b) Determine the strength of the magnetic field.

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Problem: Patients undergoing an MRI scan occasionally report seeing flashes of light. Some practitioners assume that this results from electrical stimulation of the eyes by the emf induced by the rapidly changing fields of an MRI solenoid. We can do a quick calculation to see if this is a reasonable assumption. The human eyeball has a diameter of about 25 mm. Rapid changes in current in an MRI solenoid can

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Problem: A 5.0-cm-diameter loop of wire has resistance 1.2 Ω. A nearby solenoid generates a uniform magnetic field perpendicular to the loop that varies with time as shown in the figure. Graph the magnitude of the current in the loop

mm. Rapid changes in current in an MRI solenoid can

produce rapid changes in the magnetic field, with B/t as large as 50 T/s. How much emf would this induce in a loop circling the eyeball? How does this compare with the 15 mV necessary to trigger an action potential?

Problem: A 1000-turn coil of wire 2.0 cm in diameter is in a magnetic field that drops from 0.10 T to 0 T in 10 ms. The axis of the coil is parallel to the field. Determine the emf in the coil.

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the figure. Graph the magnitude of the current in the loop over the same time interval.

Problem: A 100-turn, 8.0-cm-diameter coil is made of 0.50-mm diameter copper wire. A magnetic field is perpendicular to the coil. At what rate must B increase to induce a 2.0 A current in the coil?

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Problem: The loop in the figure is being pushed into the 0.20 T magnetic field at a speed of 50 m/s. The resistance of the loop is 0.10 Ω. Determine the direction and magnitude of the current in the loop.

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