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# L22_Viet_Faraday&Acirc;&brvbar;s Law - Physics 122...

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Physics 122 Electricity and Magnetism Lecture 22 Faraday’s Law

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05/12/09 Physics 122B - Lecture 22 2 Faraday’s Law m B dA BA Blx Φ = = = E r r m d d dx Blx Bl dt dt dt Φ = = dx Blv Bl dt = = E m Therefore, d dt Φ = E This is Faraday’s Law . It can be stated as follows: An emf E is induced in a conducting loop if the magnetic flux Φ m through the loop changes with time, so that E = |d Φ m /dt| for the loop. The emf will be in the direction that will drive the induced current to oppose the flux change, as given by Lenz’s Law. Consider the loop shown:
05/12/09 Physics 122B - Lecture 22 3 Example : Electromagnetic Induction in a Circular Loop The magnetic field shown in the figure decreases from 1.0 T to 0.4 T in 1.2 s. A 6.0 cm diameter loop with a resistance of 0.010 Ω is perpendicular to the field. What is the size and direction of the current induced in the loop? 2 2 m ( ) d d r B dB r dt dt dt π Φ = = = E 0.6 T 0.50 T/s 1.2 s dB B dt t - = = = - 2 2 -3 (0.03 m) (0.50 T/s) 1.41 10 V dB r dt = = = E -3 (1.41 10 V) 0.141 A (0.010 ) I R d = = = E The current direction is such as to reinforce the diminishing B field. Therefore, the current I will be clockwise. I

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05/12/09 Physics 122B - Lecture 22 4 Example : Electromagnetic Induction in a Solenoid A 3.0 cm diameter loop with a resistance of 0.010 Ω is placed in the center of a solenoid. The solenoid is 4.0 cm in diameter, 20 cm long, and is wound with 1000 turns of square insulated wire. The current through the solenoid wire as a function of time is shown in (b). Find the induced current in the loop. 0 sol NI B l μ = 0 sol m ANI BA l Φ = = 0 sol 6 sol 1.97 10 m d AN dI dt l dt dI dt - Φ = = = E sol 10 A/s until t=1.0 s and =0 after that. dI dt = 5 1.97 10 V until t=1.0 s and =0 after that. - = E loop / 1.97 mA until t=1.0 s and =0 after that. I R = = - E
05/12/09 Physics 122B - Lecture 22 5 What does Faraday’s Law Tell Us? Faraday’s Law tells us that all induced currents are the associated with a changing magnetic flux. There are two fundamentally different ways to change the magnetic flux through a loop: (1) The loop can move, change size, or rotate, creating motional emf;

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