Dr. Jie Zou PHY 1161 1

Chapter 23

Magnetic Flux and Faraday’s Law of Induction (Lecture I)

Dr. Jie Zou PHY 1161 2

Outline

Experimental observations of magnetic induction

Explanation for magnetic induction Magnetic flux Faraday’s law of induction A Real World Application: A

Dynamic Microphone

Dr. Jie Zou PHY 1161 3

Faraday’s Experiment on Magnetic Induction

Michael Faraday’s experimental observations:

An emf is induced in the secondary circuit when the switch in the primary circuit is changed from open to closed or from closed to open.

The induced emf produces a current in the secondary circuit as detected by the ammeter.

If the current in the primary circuit does not change (for example, when the switch remains closed), there is no induced current in the secondary circuit.

Dr. Jie Zou PHY 1161 4

Classroom Demonstration of Induced emf

Induced current produced by a moving magnet. (a) Magnet moves toward the coil, induced current

flows in one direction. (b) Magnet is held still, no induced current. (c) Magnetic moves away from the coil, induced

current flows in the other direction.

Dr. Jie Zou PHY 1161 5

Explanation for Magnetic Induction

An emf is induced in a coil when the magnetic flux through it changes with time.

Magnetic flux: a measure of the number of magnetic field lines that cross a given area.

Definition of magnetic flux, : = (B cos)A = BA cos Special cases: = 0° and 90° B: the magnetic field. A: the area. : the

angle between the magnetic field and the normal to the surface.

SI units: T·m2 = weber (Wb) A change in any of the following: B, A, and

(or) , results in a change in the magnetic flux.

Dr. Jie Zou PHY 1161 6

Example 23-1 Consider a circular

loop with a 2.50-cm radius in a constant magnetic field of 0.625 T. Find the magnetic flux through this loop when its normal makes an angle of (a) 0°, (b) 30.0°, (c) 60.0°, and (d) 90.0° with the direction of the magnetic field B.

Dr. Jie Zou PHY 1161 7

Faraday’s Law of Induction Faraday’s law of induction:

N: the number of loops in a coil. The induced emf is proportional to the rate at

which the magnetic flux changes with time, i.e., /t.

The “-” indicates that the induced emf opposes the changes in the magnetic flux.

Example 23-2: A bar magnet is moved rapidly toward a 40-turn, circular coil of wire. As the magnet moves, the average value of B cos over the area of the coil increases from 0.0125 T to 0.450 T in 0.250 s. If the radius of the coil is 3.05 cm, and the resistance of its wire is 3.55 , find the magnitude of (a) the induced emf and (b) the induced current.

t

)( initialfinal

Nt

N

Dr. Jie Zou PHY 1161 8

A Real World Application: A Dynamic Microphone

Dr. Jie Zou PHY 1161 9

Homework #8

Chapter 23, P. 828-829, Problems: #2, 5, 9, 16 (Physics, Walker, 4th edition).