Determine the net Force magnitude and direction acting on wi

Determine the net Force (magnitude and direction) acting on wire 3 due to wires 1 & 2 for the currents shown: Each wire has a horizontal length of 60 cm.

Solution

Here,

I1 = 8 A

I2 = 12 A

I3 = 10 A

d = 2 cm

L = 0.60 m

taking upwards as positive direction

Now , for the net force on the wire 3

Force = -u0 * I3 * I2*L/(2 * pi * d) + u0 * I1 * I3* L /(4 * pi * d)

Force = 4pi *10^-7 * 10 * 0.60/(6.282) * (- 12/.02 + 8/(2 * 0.02) )

Force = -4.801 *10^-3 N

the net force on the wire 3 is 4.801 *10^-3 N in downwards direction