Chapter 33 - 33.1. Model: A magnetic field is caused by an...

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33.1. Model: A magnetic field is caused by an electric current. Visualize: Please refer to Figure EX33.1. Solve: The magnitude of the magnetic field at point 1 is 2.0 mT and its direction can be determined by using the right-hand rule. Grab the current carrying wire so that your thumb points in the direction of the current. Because your fingers at point 1 point into the page, 1 B G = (2.0 mT, into the page). At point 2, the magnetic field due to the bottom wire is into the page. The right-hand rule tells us that the magnetic field from the top wire is also into the page. At point 2, 2 B G = (4.0 mT, into the page).
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33.2. Model: A magnetic field is caused by an electric current. Visualize: Please refer to Figure EX33.2. Solve: The current in the wire is directed to the right. B 2 = 20 mT + 20 mT = 40 mT because the two overlapping wires are carrying current in the same direction and each wire produces a magnetic field having the same direction at point 2. B 3 = 20 mT – 20 mT = 0 mT, because the two overlapping wires carry currents in opposite directions and each wire produces a field having opposite directions at point 3. The currents at 4 are also in opposite directions, but the point is to the right of one wire and to the left of the other. From the right-hand rule, the field of both currents is out of the page. Thus B 4 = 20 mT + 20 mT = 40 mT.
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33.3. Model: The magnetic field is that of a moving charged particle. Visualize: The first point is on the x -axis, with θ a = 90°. The second point is on the y -axis, with b = 180°, and the third point is on the y -axis with c = 0°. Solve: (a) Using Equation 33.1, the Biot-Savart law, the magnetic field strength is ( )( )( ) () 71 9 7 15 0 a 2 2 2 10 T m/A 1.60 10 C 1.0 10 m/s sin90 sin 1.60 10 T 4 1.0 10 m qv B r μθ π −− + ×× ° == = × × To use the right-hand rule for finding the direction of , B G point your thumb in the direction of . v G The magnetic field vector B G is perpendicular to the plane of r G and v G and points in the same direction that your fingers point. In the present case, the fingers point along the ˆ k direction. Thus, 15 a ˆ 1.60 10 T. B k G (b) B b = 0 T because sin b = sin 180° = 0. (c) B c = 0 T because sin c = sin 0° = 0.
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33.4. Model: The magnetic field is that of a moving charged particle. Visualize: The first point is on the x -axis, with θ a = 90°. The second point is on the z -axis, with b = 0°, and the third point is in the yz plane with c = 45°. Solve: (a) Using Equation 33.1, the Biot-Savart law, the magnetic field strength is ( )( )( ) () 71 9 7 15 0 a 2 2 2 10 T m/A 1.60 10 C 2.0 10 m/s sin90 sin 3.2 10 T 4 1.0 10 m qv B r μθ π −− + ×× ° == = × × To use the right-hand rule for finding the direction of a , B G point your thumb in the direction of . v G Your fingers point along the – y -axis, but since the charge is negative, a B G points along the + y -axis. Thus, 15 a ˆ 3.2 10 T. B j G (b) B b = 0 T because sin b = sin 0° = 0.
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This note was uploaded on 01/30/2011 for the course PHYS 131 taught by Professor E.salik during the Winter '10 term at Cal Poly Pomona.

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Chapter 33 - 33.1. Model: A magnetic field is caused by an...

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