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Transcript

AMERICAN UNIVERSITY OF SHARJAH COLLEGE OF ARTS AND SCIENCES Dept. of Physics PHY 102 – Fall 2006 Midterm 3 – December 10, 2006 Duration: 50 minutes (Class time) Name: _______________________ ID #: _________________________ Question Maximum grade 1 10 2 10 3 10 Your grade 1) For the two current carrying wires shown in figure (I1 is out of the page), determine from basic principles (Ampere’s law or Biot-Savart law) (a) the magnetic field created by each current at point O2 and (b) the total magnetic field at point O2. (use = 30o, R1 = 4 cm, R2 = 10 cm I1 = 10 A and I2 = 5 A). I dl rˆ Biot-Savart Law: dB 0 0 4 107 T m/A ; Ampere's law : B dl 0 I net 2 4 r loop To find the magnetic field, B1, created by I1, apply Ampere’s law: Ampere’s loop is a circle of center O1 and of radius R1/2. B1 2R1 / 2 0 I net R12 I net I 1 I1 / 4 ( R1 / 2) 2 I B1 0 1 2.5 10 5 T 4R1 The direction of B1 at O2 is to the left To find the magnetic field, B2, created by I2, apply Biot-Savart law. Magnetic field at point O2 created by segment “ab” is zero because dl rˆ 0 . Magnetic field at point O2 created by segment “cd” is zero because dl rˆ 0 . Magnetic field at point O2 created by the arc “bc”: here dl rˆ sin(90)dl k dl k I B2 0 22 dl 4 R I I /6 I B2 0 22 dl 0 22 Rd 0 2 2.62 106 T (out of page) 0 4 R 4 R 24 R The total magnetic field at point O2 is B = - 2.5 10 5 T i + 2.62 10 6 T k. The magnitude of this vector is B (2.5 10 -5 ) 2 (2.62 10 -6 ) 2 2.5110 -5 T 2) The figure shows a cross section of three parallel wires each carrying a current of 20 A. The currents in wires A and B are out of the paper, while that in wire C is into the paper. If the distance R = 5 mm, what is the magnitude of the force on a 2 m length of wire A? B R A R C F IL B where L = 2k and B is the total magnetic field created by Ib and Ic at the location of wire A. I B 0 i j 8 10 4 i j 2R F 3.2 10 2 (i j ) F 4.53 10 2 N 3) A circular coil (radius = 15 cm) with a total resistance of 4 is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. a) If B varies with time according to B = B0 sin (t), where B0 = 80 µT and = 50 rad/s, calculate the current induced in the coil at t = 0.020 s? b) If the coil starts rotating in this varying field B = B0 sin (t), calculate the current induced in the coil at an instant when the angle between the field and the normal to the plane of the loop is equal to 30° and increasing at a constant rate of 18°/s. I R d dt BA cos( ) In part (a) = 0, only B changes with time: dB AB0 cos(t ) dt At t = 0.02 s, 8.9 10 4 V and I = 2.23×10-4A A In part (b) both B and change with time: dB d A cos( ) AB sin( ) AB0 cos(t ) cos( ) AB0 sin(t ) sin( ) dt dt Where d 18 0 / s 0.1rad / s dt t The angle between the field and the normal to the plane of the loop is equal to 30° at t / 30 / 18 1.67 s = 3.86 ×10-4 V I = 9.6 ×10-5 A