Question

Two long straight parallel wires, standing on air 2m apart carry currents i1 and i2 in the same direction. The magnetic intensity at a point mid way between the wires of 7.95 AT/m. If the force on each wire per unit length is 2.4 × 10-10. Evaluate i1 and i2

Answer 1

Given:

$d=2\;\rm m$

$H=7.95\:\rm A/m$

$F/l=2.4*10^{-10}\:\rm N$

The magnetic intensity at a point mid way between the wires

$$H=H_1+H_2=\frac{I_1}{2\pi d/2}+\frac{I_1}{2\pi d/2}$$

$$H=\frac{I_1+I_2}{\pi d}$$

The force on each wire per unit length

$$F/l=\mu_0\frac{I_1I_2}{2\pi d}$$

Using these equations, we get

$$I_1+I_2=2\pi*7.95\\ I_1*I_2=2*2.4*10^{-10}/10^{-7}$$

$$I_1+I_2=50\\ I_1*I_2=0.0048$$

Roots:

$$I_1=50\:{\rm A},\quad I_2=9.6*10^{-5}\:\rm A$$