Two Thin Long, Parallel Wires Separated By A Distance D Carry A Current I Each In The Same Direction. They Will

The force per unit length between two long current-carrying conductors is

\( F = \frac{\mu_{0}i_{1}i_{2}}{2\pi d} \)

where:

d is the distance between the conductors and

\( i_{1} and i_{2} \) are the currents carried by the conductors.

The conductors attract each other if \( i_{1} and i_{2}\) are in the same direction. The magnetic field created by conductor 1 at the location of the conductor 2, where the conductor 2 gets attracted towards conductor 1.

Since \( i_{1} = i_{2} = i\)

Therefore, they will attract each other with a force per unit length of

F = \( \frac{\mu_{0}i^{2}}{2\pi d}\)

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