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hw13 - Physics 21 Fall 2004 Solution to HW-13 28 P 18 Two...

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Physics 21 Fall, 2004 Solution to HW-13 28 P 18 Two long parallel wires 7.0 cm apart carry 16.5 A currents in the same direction. Determine the magnetic field strength at a point P 12.0 cm from one wire and 13.0 cm from the other. α β α α π/2 − α B B 1 β β π/2 − β B 2 The field B at the point P will be the vector sum of the fields from the two wires. We must find the components of the two fields so we can add them. We can use the Law of Cosines to solve for the angles α : 13 2 = 12 2 + 7 2 2(12)(7) cos α α = 81 . 79 12 2 = 13 2 + 7 2 2(13)(7) cos β β = 66 . 01 The magnitude of the fields are obtained from B = µ 0 I/ 2 πR , where R 1 = 0 . 012 m for the left wire and R 2 = 0 . 013 m for the right wire. The diagrams show how we can use geometry to find the components of B 1 and B 2 : B 1 = µ 0 I 2 π (0 . 12 m) cos( π/ 2 α ) ˆ i + sin( π/ 2 α ) ˆ j B 2 = µ 0 I 2 π (0 . 13 m) cos( π/ 2 β ) ˆ i sin( π/ 2 β ) ˆ j Subsituting the numbers, we find B = B 1 + B 2 = ( 5 . 04 ˆ i 0 . 64 ˆ j ) × 10 5 T 28 P 32 A small loop of wire of radius 1.8 cm is placed at
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