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Faraday’s Law 10 5T 10 m As the bar moves a current is induced! 3 m/s 2m dB E dt There are no batteries anywhere, so we say that a current is induced, by an induced emf. Hence, an electric current can be induced in a circuit by a changing magnetic field, in the opposite direction to the change in flux. Generality of Faraday’s Law •Faraday’s law applies when moving a wire in a magnetic field dB E dt However, changing magnetic fields also produce an EMF. What is the nature of the force? It is not a magnetic force because the charges are not necessarily moving Changing magnetic fields must produce electric fields! Faraday’s Law and Electric Fields dB E dt q E E ds dB E ds dt Faraday’s Law and Electric Fields dB E ds dt . A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its axis. The field is 0 outside the cylinder. If the field is changing at the rate 0.60 T/s, the electric field induced at a point 2R from the cylinder axis is: Using Faraday’s law: 2p (2R)E =-p(R2) dB/dt, so E= (-(R2) /4) dB/dt=0.0045 V/m Comparision of Induction dE B ds 0 I 0 0 dt dB E ds dt •No magnetic monopole, hence no magnetic current •Electric fields and magnetic fields induce in opposite fashions What is the combined resistance of the mess at right? A) 1.5 k B) 12 k C) 14 k D) 21 k 9 k 3 k 3 k 6 k 3 k 2 k R R1 R2 3 3 6 1 1 1 1 1 1 R R1 R2 3 6 2 R R1 R2 R3 3 9 2 14 3 k A Multiloop Circuit I1 + I3 = I2 1.5 – 3I2 = 0 9 – 5I1 – 3I2 = 0 I2 = 1.5/3 = 0.5 A I1 = (9 – 3I2)/5 = 1.5 A I3 = I2 – I1 = 0.5 – 1.5 = – 1 A I1 – + 9V 5 I2 3 1.5 V – + I3 What Whatisisthe thevoltage conservation loop rule of you current get applied law associated to the upper with loop? the junction on the right? A) A) 9I1++5II21 =+ I3I 32=0 B) B) 9I+1 +5II13 –=3I I22 = 0 C) C) 9I–2 +5II13+=3I I12 = 0 D) D) 9I1–+5II21 + – 3I I3 2==00 Odd Circuit What is the current through the resistor? A) 3.6 A B) 1.8A C) 90 A D) 0 A – + 9V 5 9V – + Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open. The values of the emf , resistance R, and the capacitance C for each of the circuits are circuit 1: 18 V, R = 3 , C = 1 µF circuit 2: circuit 3: 18 V, R = 6 , C = 9 µF 12 V, R = 1 , C = 7 µF circuit 4: 10 V, R = 5 , C = 7 µF Which circuit has the largest current right after the switch is closed? Which circuit takes the longest time to charge the capacitor to ½ its final charge? Which circuit takes the least amount of time to charge the capacitor to ½ its final charge? Torque on a Loop B=1T 2 cm I = 1A What is the torque on the wire? A) 4p10-2Nm D) p10-4Nm B) p10-2Nm C) 4p10-4Nm Which direction does the torque twist the loop? A) Right towards, left away B) Right away, left towards C) Top towards, bottom away D) Bottom towards, top away Quiz: Ampere’s Law •Consider three wires with current flowing in/out as shown •Consider three different loops surrounding the wires X Y Which of the loops has the largest and smallest integrals of the magnetic field around the loops drawn? A) X > Y > Z C) Y > Z > X B) X > Z > Y D) Y > X > Z 2A 3A 1A Z Quiz A)Remains the same B) Reverses C) Changes in magnitude but not direction D)Changes to some other direction