Brennen Hawkins

2023-03-11

Two parallel wires carry currents of 20 A and 40 A in opposite directions. Another wire carrying a current antiparallel to 20 A is placed midway between the two wires. The magnetic force on it will be
Towards 20 A
Towards 40 A
Zero
Perpendicular to the plane of the current

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The magnetic field produced by both the couple of wires (AC and BC) will be in the same direction going inside the plane as shown in the diagram by the right hand rule if A is the wire carrying current of 20 A, B is the wire carrying current of 40 A in the opposite direction, and C is the middle wire carrying current antiparallel to 20 A.
$\stackrel{\to }{F}=I\left(\stackrel{\to }{L}×\stackrel{\to }{B}\right)$
According to the cross product, the force on the wire will be to the right because of wire B and to the right because of wire A. Therefore, the sum of the two forces will result in a force that is toward the right, or toward the 40 A current-carrying wire.
Additionally, we are aware that parallel wires carrying current in the same direction attract one another while those carrying current in the opposite way repel one another. That rule also leads to a net force of 40 A flowing in the direction of wire B.

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