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As show below, an infinitely long wire carries a current t_1 = 10.0A in the +y (

ID: 1515378 • Letter: A

Question

As show below, an infinitely long wire carries a current t_1 = 10.0A in the +y (upward) direction. A second parallel wire of finite length carries a current t_2 = 8.0A in the -y (downward) direction. There is also a third infinitely long parallel wire that initially carries no current (I_2 = 0.0A initially): Show how you find the magnitude of the force F_2, that current I_x exerts on the segment of wire carrying current I_2. Show how you find the direction of the force F_2 that current I_2, exerts on the segment of wire carrying current I_2. Show how you find the current I_3 (magnitude and direction) that must flow in the third infinitely long wire so that the net (overall) force F_2 (due to currents l_1 and I_3, simultaneously) is 0.0N (no net force). Make sure you clearly sketch the magnitude and direction of I_3 in your BlueBook!

Explanation / Answer

given

I1 = 10 A

I2 = 8 A

d12 = 2 cm = 0.02 m

Length of segment, L = 5 cm = 0.05 m

a) F12 = mue*I1*I2*L/(2*pi*d12)

= 4*pi*10^-7*10*8*0.05/(2*pi*0.02)

= 4*10^-5 N

b) Direction of force : towards right

because, anti parallel current carrying wires repel each other.

c)

Apply, net force wire 2 = 0

F12 - F32 = 0

F32 = F12

mue*I2*I3*L/(2*pi*d23) = 4*10^-5

I3 = 4*10^-5*(2*pi*0.03)/(4*pi*10^-7*8*0.05)

= 15 A

direction : upward