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PHYSICS 2020 CAPA 9

PHYSICS 2020 CAPA 9 - PHYS2020 Fall 2006 CAPA Set 9 1[1pt A...

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PHYS2020, Fall 2006 CAPA Set 9 1. [1pt] A vertical straight wire carrying an upward 11.3 A current exerts an attractive force per unit length of 8 . 00 × 10 - 4 N/m on a second parallel wire 7.70 cm away. What is the magnitude of the current that flows in the second wire? The current in the first wire creates a magnetic field which acts on the current in the second wire. The magnetic field created by a current along a long straight wire is given by B = μI 2 πr . Labeling the current in the first wire as I 1 the field is B = μ 0 I 1 2 πr . The force that this magnetic field exerts on the second wire is given by F = IlscriptB . Here the current is that which is carried in the second wire I 2 so the force on the second wire is F 2 = I 2 lscript 2 B where B is given from before so we have F 2 = I 2 lscript 2 μ 0 I 1 2 πr . We are asked to find the current flowing in the second wire so we solve for I 2 to get I 2 = F 2 · 2 πr lscript 2 μ 0 I 1 . We don’t know F 2 or lscript 2 but we do know F 2 /lscript 2 which is all that is necessary to solve the problem. For the numbers given here, the final answer is I 2 = F 2 lscript 2 2 πr μ 0 I 1 = 8 . 00 × 10 - 4 N/m 2 π 0 . 0770 m 4 π × 10 - 7 T m/A · 11 . 3 A = 8 . 00 × 10 - 4 N/m 0 . 0770 m 2 × 10 - 7 T m/A · 11 . 3 A = 27 . 3 A . 2. [1pt] Determine the magnitude of the magnetic field midway between two long straight wires 1.80 cm apart when one wire carries 5.40 A and the other carries 15.5 A . Assume these currents are in the same direction.
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