AP Physics III.E

Electromagnetism

22.1 Induced EMF and Induced Current

Astounding demo.

Induced EMF (electromagnetic induction) from

• Changing magnetic field

• Changing the area of the coil

22.2 Motional EMF

EMF induced in a moving conductor

The separated charges on the ends of the moving conductor

create an induced EMF or motional EMF. Note, the EMF

is induced only when the conductor is moving.

“And the formula is . . . (drum roll please)”

Ex. The rod in the illustration has a velocity of 5.0 m/s perpendicular to a magnetic field with a strength of 0.80 T. The length of the rod is 1.6 m and the bulb has a resistance of 96 Ohms. Find a) the EMF b) the induced current c) the electric power dissipated by the bulb and d) the energy used by the bulb in 60.0 s.

Motional EMF and Electrical Energy (another magnetic force

to worry about)

Ex. What is the force (magnitude and direction) on the rod in the previous direction?

The force on the conductor is in the opposite direction of the velocity. So where does the force come from the light the

bulb for 60 s?

Ex. An external agent provides 0.086 N of force to keep the rod moving at 5.0 m/s for 60.0 s. Find the work done by the force.

The direction of current and conservation of energy.

Conceptual Example 3.

p. 700: 2, 4-7, 9

2. a) yours b) 3.0 m

4. 7800 V

6. 3.2 A (recall formula for R in terms of resistivity)

22.3 Magnetic Flux

Any induced EMF can be described in terms of magnetic flux. Magnetic flux – the product of the strength of

the magnetic field and its cross-sectional area. φ = BA (measured in

Webers)

A derivation

General expression for magnetic flux.

Ex. A conducting coil is in a magnetic field of 0.50 T. The area of the coil is 2.0 square meters. Find the flux for angles of 0.0º, 60.0º and 90.0º.

22.4 Faraday’s Law of Electromagnetic Induction

Ol’ Michael (as well as Joseph Henry) found that whenever there is a change in flux through a loop

of wire, an EMF is induced inside the loop. Faraday’s law unites flux and a time interval.

Faraday’s Law of electromagnetic induction

EMF is generated if magnetic flux changes for any reason. So change in flux depends on the

change in the magnetic field, area or angle.

Ex. A coil of wire with 20 turns has an area of 1.5 EE –3 square meters. A magnetic field is perpendicular to the surface of each loop at all times. At the initial time, the initial magnetic field is 0.050 T. At 10.0 s the magnetic field is 0.060 T. Find a) the average induced emf during this time and b) the average induced emf if the magnetic field decreases from 0.060 T to 0.050 T in 0.10 s.

Ex. A coil of wire has an area of 0.020 square meters with 50 turns. At initial time the coil is oriented so that the normal of the surface of the coils is parallel to a magnetic field of 0.18 T. At 0.10 s, the angle is 30.0º to the normal. Find a) the induced emf. b) What is the induced emf if the coil is returned to its initial orientation in 0.10 s?

p. 701: 10-11, 17-21; Rev. 07B1, 2

10. a) 0.0056 Wb b) 0 Wb

18. 2.8 EE -3 V

20. 1.5 m2/s

B1

a) 8.8 m/s b) drawing c) 63 N d) 0.27 e) yrz

B2

a) ? b) ? c) 1.7 EE 5 m/s d) 6500 V

22.5 Lenz’s Law

The polarity of a magnetic field in a coil results from

• The original magnetic field that produces the changing flux that leads to the emf.

• The induced current that creates its own magnetic field

Lenz’s Law – the induced emf resulting from changing magnetic flux leads to an induced current whose direction is such that the induced magnetic field opposes the direction of the original flux

change.

Strategy

• Determine if the flux that penetrates the coil is increasing or decreasing

• Find the direction of the induced magnetic field. It must be in a direction that opposes the change in flux.

• Once the direction of the induced magnetic field is determined, use RHR-2 to determine the direction of the induced current.

A couple of examples.

78B4, 07B3, 07B4

78B4a) 1.5 m/s to the ?b) 8 Nc) 12 Wd) 4.5 J07B3a) Yoursb) Yours again

c) 533 Ohmsd) 0.15 Ae) 6.0 EE -6 F07B4a) 6 EE -6 m3/sb) Q = Av is also vol. flow

rate (2.4 m/s)a) Bernoulli’s Eq. (0.29

m)b) Yours