Question

Two long, parallel, current-carrying wires lie in an xy-plane. The first wire lies on the line y = 0.300 m and carries a current of 26.0 A in the +x direction. The second wire lies along the x-axis. The wires exert attractive forces on each other, and the force per unit length on each wire is 295 µN/m. What is the y-value (in m) of the line in the xy-plane where the total magnetic field is zero?

Answer 1

The y-value is z = 0.759 m

Step-by-step explanation:

From the question we are told that

The position of the first y-axis is
`y_1 = 0.300 \ m`

The current on the first wire is
`I_ 1 = 26.0 \ A`

The force per unit length on each wire is
`(F)/(l) = 295 \mu N/m = 295 * 10^(-6) \ N/m`

Generally the force per unit length on first wire is mathematically represented as

`(F)/(l) = (\mu_o * I_1 * I_2 )/(2*\pi* y_1)`

Where
`\mu _o` is the permeability of free space with value
`\mu_o = 4\pi * 10^(-7) N/A^2`

substituting values

`295 *10^(-6) = ( 4\pi * 10^(-7) * 26.0 * I_2 )/(2 *3.142* 0.300)`

`I_2 = (295 *10^(-6 ) * 0.300 * 2* 3.142 )/( 4\pi * 10^(-7) * 26 )`

`I_2 = 17.0 \ A`

Now the at the point where the magnetic field is zero the magnetic field of each wire are equal , let that point by z meters from the second wire on the y-axis so

`(\mu_o I_2)/(2 * \pi * y_1) = (\mu_o I_1)/(2 * \pi * (y_1-z))`

`I_2 (y_1 - z) = I_1 * y_1`

substituting values

`17.0 ( 0.300 - z) = 26 * 0.300`

z = 0.759 m