Solutions _E2 - Physics 204, summer 2008 Exam #2 practice...

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Physics 204, summer 2008 Exam #2 practice problems solutions 1. A current flows upward in a long straight wire. To the right is a rectangular loop that is also carrying a current (the power supply is not shown so the diagram doesn’t get too cluttered). Predict the magnetic force the straight wire exerts on the rectangular loop. I need to break the loop into 4 straight segments. The magnetic force on the top segment will point up. The magnetic force on the bottom segment will point down and is equal in magnitude to the magnetic force on the top segment, so they cancel. The force on the left segment points to the left, and the force on the right segment points to the right. These do not cancel because the magnetic field is stronger closer to the straight wire. I’ll call the current in the straight wire and the current in the loop . wire loop I I () ,, 00 0 7 5 sin 90 sin 90 22 11 2 4 10 5.00 14.0 0.20 2 0.026 0.10 7.96 10 B B L B R loop L loop R wire wire B loop L R loop LR loop wire B B B FF F I L B I L B II FI L B B I L rr IIL F Tm A A A m F mm FN μμ ππ μ π =+= ° + ° ⎛⎞ ⇒= = ⎜⎟ ⎝⎠ × × The minus sign indicates the force is to the left. 2. Two long straight wires are carrying currents in opposite directions as shown in the diagram. a. Predict the magnitude and direction of the magnetic field at each of the 3 points shown. b. Will the wires be attracted to each other, repelled by each other, or not exert a force on each other at all? Explain in detail the reasoning behind your choice. The magnetic field at each point is a superposition of the contributions to th hand “grab the wire” rule sets the direction for each of these contributions. The positive z direction will be out of the page and the negative z direction will be into the page. The subscript R represents the right traveling current and subscript L the left traveling current. For point 1 e magnetic field from each wire. The right the , 1 , 0 1, 7 5 1, 2 41 0 1 0 6.67 10 2 0.02 0.06 RL z R L z BB B I B r r TmA A BT =+ + = ×⋅ = × r For point 2
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() 22 , 2 , 00 0 2, 7 4 11 2 41 0 1 0 2.00 10 2 0.02 0.02 RL z R L z BB B II I B rr r r TmA A B T mm μμ μ ππ π =+ ⎛⎞ ⇒= + = ⎜⎟ ⎝⎠ ×⋅ = −× r For point 3 33 , 3 , B 0 3, 7 5 3, 2 0 1 0 6.67 10 2 0.06 0.02 z R L z I B r r A B T + = + + = × r The wires are repelled by each other. For example, the magnetic field created by the bottom wire points into the page where the top wire is located. Since the current in the top wire is to the right you can use the right hand rule for the magnetic force on the moving charges. Since the charges are moving to the right, and the magnetic field points down, the magnetic force on those charges is up. This means the top wire is repelled by the bottom wire. Newton’s 3 rd law says the bottom wire will feel a force opposite in direction to this (down) and be repelled from the top wire.
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This note was uploaded on 10/04/2009 for the course PHYSICS 750:204 taught by Professor Croft during the Summer '08 term at Rutgers.

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Solutions _E2 - Physics 204, summer 2008 Exam #2 practice...

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