Question

two long parallel transmission lines 40.0 cm apart carry 20.0 A and 71.0 A currents.

a) find all locations where the net magnetic field of the two wires is zero if these currents are in tbe same direction.

please enter your answer as a distance from the wire carrying 20.0 A

b) find all locations where the net magnetic field of the two wires is zero if these currents are in opposite directions.

please enter answer as two distances the first distance from the wire carrying 20.0 A, and the second distance from the wire carrying 71.0 A

Answer 1

a)
The net magnetic field will be zero between the wires.
Net field, B = oI1/2r - oI2/2(40 - r) = 0
Where I1 = 20 A and I2 = 71 A and r is the point where the net magnetic field becomes zero.
I1/r = I2/(40 - r)     [Cancelling o/2 on both sides,
20/r = 71/(40 - r)
800 - 20r = 71r
91r = 800
r = 8.97 cm

b)
The net magnetic field will be zero near 20 A wire, but outside the space between the wires.
Net field, B = oI1/2r - oI2/2(40 + r) = 0
Where I1 = 20 A and I2 = 71 A and r is the point where the net magnetic field becomes zero.
I1/r = I2/(40 + r)     [Cancelling o/2 on both sides,
20/r = 71/(40 + r)
800 + 20r = 71r
51r = 800
r = 15.686 cm (From 20 A wire)

From 71 A wire, the distance is,
s = 15.68 + 40
= 55.686 cm