Question

A current of 10A passes through two very long wires helf parallel to each other and separated by a distance of 1m.what is the force per unit length between them?

Answer 1

F/L=u°(I1)(I2)/2(pi)d
=(4(pi)×10^(-7)×10×10)/2 (pi)×1
=2×10^(-7)×10×10
=2×10^(-7)×10^(2)
=2×10^(-5) Newton/meter

Answer 2

The force per unit length between wires is $2\times10^-^5N/m$.

Explanation:

The force between two parallel wire give by

$\frac{F}{l} =\frac{\mu_0i_1i_2}{2\pi d}$

Here, d is the separation between the wires and $i_1,i_2$ are the carrying currents in both the parallel wires.

Given d = 1 m,  $i_1=i_2= 10A$ and take constant value, $\mu_0=4\pi\times10^-^7T.m/A$

substitute the given values, we get

$\frac{F}{l} =\frac{4\pi\times10^-^7T.m/A\times10A\times10A}{2\pi\times1m}$

$\frac{F}{l} =200\times10^-^7N/m$

$\frac{F}{l} =2\times10^-^5N/m$.

Thus, the force per unit length between wires is $2\times10^-^5N/m$.

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