An example of electromagnetic induction:

Chapter 25 Electromagnetic Induction and Electromagnetic WavesWednesday, March 24, 20103:16 PM

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Faraday's further investigations of electromagnetic induction:

Here's another example of EM induction:

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And here's a final example of EM induction:

Faraday concluded from his investigations that a changing magnetic field induces an electromotive force (i.e., emf, which is another way of saying a potential difference) in a nearby electric circuit, which ultimately causes electric current to flow in the circuit.

To make this relationship quantitative, we need the

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To make this relationship quantitative, we need the concept of magnetic flux, which we'll discuss next.

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There are three ways the magnetic flux through a coil of wire can change: The strength of the magnetic field can change, the area of the coil can change, or the relative orientation of the coil and the magnetic field (i.e., the angle theta) can change.

The following two diagrams illustrate Lenz's law:

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There is also an alternative version of the right-hand rule that is convenient when the vectors are not perpendicular. For example, to determine the direction of the force on a positively charged particle when the velocity of the particle and the magnetic field are not perpendicular, it's simpler to curl your fingers from the velocity vector to the magnetic field vector through the acute angle; then the thumb points in the direction of the force.

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CP 3 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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CP 14 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

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?

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necessary to trigger an action potential?

CP 18 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 over the same time interval.

CP 15 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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CP 21 A microwave oven operates at 2.4 GHz with an intensity inside the oven of 2500 W/m2. Determine the amplitudes of the oscillating electric and magnetic fields.

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CP 29 At what distance from a 10 W point source of electromagnetic waves is the electric field amplitude (a) 100 V/m, and (b) 0.010 V/m.

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CP 43 The spectrum of a glowing filament has its peak at a wavelength of 1200 nm. Determine the temperature of the filament in degrees Celsius.

CP 57 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?

CP 31 Only 25% of the intensity of a polarized light wave passes through a polarizing filter. What is the angle between the electric field and the axis of the filter?

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CP 58 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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