Answer to Question #235299 in Electrical Engineering for Braim016

Question #235299
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
1
Expert's answer
2021-09-10T00:03:37-0400

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\\\\\nI_1*I_2=2*2.4*10^{-10}\/10^{-7}"

"I_1+I_2=50\\\\\nI_1*I_2=0.0048"

Roots:

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


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