Question

You are given two infinite, parallel wires, each carrying current.The wires are separated by a distance, and the current in the two wires is flowing in the same direction. This problem concerns the force per unit length between the wires.

A. Is the force between the wires attractive orrepulsive?
B. What is the force per unit length between the two wires?

Answer 1

A. Attractive

B. ( μ₀I² ) / ( 2πd )

Step-by-step explanation:

A. We know that currents in the same direction attract, and currents in the opposite direction repel, according to ampere's law. In this case the current in the two wires are flowing in the same direction, and hence the force between the two wires are attractive.

B. Suppose that two wires of length
`l_1` and
`l_2` both carry the current
`I` in the same direction ( given ). In the presence of a magnetic field produced by wire 1, a force of magnitude m say, is experienced by wire 2. The magnitude of the magnetic field produced by wire 1 at distance say d, from it's axis, should thus be the following -

`B_1` = μ₀I / 2πd

The force experienced by wire 2 should thus be -

`F_2` = I(
`l_2`
`*`
`B_1` )

= I
`*`
`l_2 * B_1 *` Sin( 90 )

= I
`*`
`l_2` ( μ₀I / 2πd )

Therefore the force per unit length experienced by wire 2 toward wire 1 should be ...

(
`F_2` /
`l_2` ) = ( μ₀I² ) / ( 2πd ) ... which is our solution