1 28 magnetic induction

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3 induced currents due to magnetic force qv x B

4 Faraday’s Law induced current due to qvB force can be determined in terms of magnetic flux flux definition same as before, with B replacing E

5 Faraday’s Law emf induced around closed loop:

6 Lenz’s Law The change in externally applied magnetic flux is opposed by the responsive magnetic flux change of a circuit. indicated by (-) sign in Faraday’s Law:

7 current direction determined from Lenz’s Law

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9 Lenz’s Law: induced magnetic force opposes the motion

10 A metallic wire loop is in a uniform magnetic field. Determine if there is a current induced in the loop when loop is stationary loop moves left or right loop moves upward out of the field region

11 A wire loop moves from a region with no magnetic field into a region with a uniform magnetic field pointing into the page. What is the direction of induced current in loop?

12 The loop is now entirely inside the B-field region Apply Faraday’s Law to determine induced emf.

13 Example F.L. A loop of area 0.45 sq.m. is rotated 180 deg. in 0.15 seconds in uniform B = 1.2 tesla such that maximum flux change occurs. Calculate average emf induced.

14 flux through coil N = #turns of wire flux = NBAcos .

15 simple motor

16 Ex. The loop was inserted in 0.05s. The emf induced is = NB(  A)/t = (80)(0.6)(ax/t) = (80)(0.6)(0.2)(x/t) = (80)(0.6)(0.2)(0.15/0.05) = 28.8 volts B = 0.6T

17 motional emf

18 motional emf: Eddy Currents produce resistive force.

19 The property of an electric circuit whereby an electromotive force is produced in the circuit by a change of current in the circuit itself. (McGraw-Hill Science Dict.) self-inductance

20 SI Unit: Henry, 1 H = 1 Wb/An= #turns/m Example: n = 10,000 turns per meter, length 1.0m, and Area = 1.0m2. L = (12.6x10 -7 )(10,000) 2 (1)(1) = 126H L, solenoid

21 Magnetic Energy Example: energy stored in a 126 henry coil with 10,000A U m = ½ (126)(10,000) 2 = 6.3x10 9 J = 6.3GJ.

22 SI Unit: joule per cubic meter, J/m 3. Ex. Calculate the energy density in a 5.0T field. u m = (5) 2 /(8  x10 -7 ) = 10 MJ/m 3. energy density

RL Circuits

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26 Summary

27 Inductors have resistive and inductive voltage drops Ex. Current flow is increased through an inductor with L = 800mH and resistance r = 20 ohms at a rate of 30 amperes/second. The voltage when I = 2A is:  V = - (0.8)(30) – (2)(20) = -24 – 40 = -64 volts.

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30 F L = qv d x BF R = qE perpendicular F up = qv x B