three long straight wires are all in the xy-plane and directed parallel to the y
ID: 2091308 • Letter: T
Question
three long straight wires are all in the xy-plane and directed parallel to the y-axis. The first wire is at x=0m and has a current of .4A flowing through it in the y-direction. The second wire is at x=1.2m and there is an unknown current flowing through it. The third wire is at x=3m and has a current of 1.2A flowing through it in the negative y-direction. There are no other sources of magnetic field and the magnetic force of the third wire is zero. What is the current flowing through the second wire?Explanation / Answer
F31 = force on wire three due to wire 1
= mu*i1*i3*/(2*pi*3)
= mu*0.4*i3*/(2*pi*3)
F32 = force on wire three due to wire 2
= mu*i2*i3*/(2*pi*3)
= -mu*i2*1.2*/(2*pi*1.8)
net force on wire three =F31+F32
mu*0.4*1.2*/(2*pi*3) + mu*i2*1.2*/(2*pi*1.8) =0
i2 = 0.4*1.8/3 = -0.24
hence current in third wire is 0.24 in negative y direction
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