Use the worked example above to help you solve this problem. Two wires, each hav

Question

Use the worked example above to help you solve this problem. Two wires, each having a weight per unit length of 1.06 Times 10^-4 N/m, are parallel with one directly above the other. Assume that the wires carry currents that are equal in magnitude and opposite in direction. The wires are 0.20 m apart, and the sum of the magnetic force and gravitational force on the upper wire is zero. Find the current in the wires. (Neglect Earth's magnetic field.) Use the values from PRACTICE IT to help you work this exercise. If the current in each wire is doubled, how far apart should the wires be placed if the magnitudes of the gravitational and magnetic forces on the upper wire are to be equal?

Explanation / Answer

Here ,

let the current in each wire is I

as the magnetic force per m is given as

Fm = u0*I1 * I2/(2*pi*d)

Now , for the magnetic force to balance gravity force

4pi *10^-7 * I^2/(2 *pi *0.2) = 1.06 *10^-4

solving for I

I = 10.3 A

the current in the wires is 10.3 A
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for double current in the wire

u0*(2 * 10.3)^2/(2 *pi * d) = 1.06 *10^-6

4pi *10^-7 * (2 * 10.3)^2/(2 *pi * d) = 1.06 *10^-6

solving for d

d = 0.8 m

the distance between the wires should be 0.8 m

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