Question

Two long parallel wires 20 cm apart carry currents of 5.0 A and 8.0 A in the between the two wires where the magnetic field is zero?

a. yes, midway between the wires
b. yes, 12 cm from the 5-A wire
c. yes, 7.7 cm from the 5-A wire
d. no

Answer 1

c. yes, 7.7 cm from the 5-A wire

Step-by-step explanation:

Given;

distance between the two wires, r = 20 cm = 0.2 m

first current, I₁ = 5.0 A

second current, I₂ = 8.0 A

The magnetic field due to the two wires occurs in different directions and it can be zero at this region.

Let x be the distance from 5 A wire where the magnetic field is zero.

`B = (\mu_o)/(2\pi) [(I_1)/(x) -(I_2)/(r-x) ] = 0\\\\ (\mu_o)/(2\pi) [(I_1)/(x) -(I_2)/(r-x) ] = 0\\\\ (\mu_o)/(2\pi) [(5)/(x) -(8)/(0.2-x) ] = 0\\\\(5)/(x) -(8)/(0.2-x) = 0\\\\(5)/(x) = (8)/(0.2-x)\\\\5(0.2-x) = 8x\\\\1 -5x = 8x\\\\1 = 5x \ + \ 8x\\\\1 = 13x\\\\x = (1)/(13) \\\\x = 0.077 \ m\\\\x = 7.7 \ cm`

Therefore, the correct option is c. yes, 7.7 cm from the 5-A wire