Two long straight wires run parallel to each other. Steady currents I 1 = I 2 =

Question

Two long straight wires run parallel to each other. Steady currents I1 = I2 = 1.0 A flow in the wires in the directions shown below. Let B1 be the magnetic field of I1 and B2 be the magnetic field of I2.

a.) Sketch the magnetic field vectors B1 and B2 to show the directions of the fields at the point PA. Then determine the magnitude and direction of the net magnetic field at PA.

b.) Sketch the magnetic field vectors B1 and B2to show the directions of the fields at the point PB. Then determine the magnitude and direction of the net field at PB.

c.) Determine the magnitude of force per unit length on I1 due to I2.

Explanation / Answer

a) From RHR, B1 will be upward and B2 will be downward at PA. As the distance and I1 = I2 are same , so the net magnetic field will be zero at PA.

b) From RHR, B1 and B2 both will be upward at PB, so the net magnetic field will add up at PB.

B = B1 + B2 = uo*I1/2pi*r1 + uo*I2/2pi*r2

= 2*10^-7*1[1/0.45 + 1/0.15] = 1.78*10^-6 T (Upward)

c) The  force per unit length = F/L = (uo*I1*I2)/(2pi*r)

F/L = (2*10^-7*1*1)/0.3 = 6.67*10^-7 N (Attractive)

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