Question

derive the relation for the force per unit length between two infinity long,parallel, straight conductors carrying current ​

Answer 1

The force is $\dfrac{I_{b}L\mu_{0}I_{a}}{2\pi d}$

Explanation:

Given that,

The force per unit length between two infinity long,parallel, straight conductors carrying current.

Two long parallel conductors a and b separated by a distance l and carrying currents $I_{a}$ and $I_{b}$ respectively.

Using ampere's law

$B_{a}=\dfrac{\mu_{0}I_{a}}{2\pi d}$

Conductor B will experience a sideways force because of conductor a.

Let this force is $F_{ba}$

$F_{ba}=I_{b}LB_{a}$

Put the value of B

$F_{ba}=\dfrac{I_{b}L\mu_{0}I_{a}}{2\pi d}$

By symmetry,

$F_{ba}=-F_{ab}$

Hence, The force is $\dfrac{I_{b}L\mu_{0}I_{a}}{2\pi d}$

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Topic : force

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