Two long parallel transmission lines 35.0cm apart carry 23.5A and 77.5A currents

Question

Two long parallel transmission lines 35.0cm apart carry 23.5A and 77.5A currents

Part A

Find all location where the net magnetic field of the two wires is zero if these currents are in the same direction.

Please, enter your answer as a distance from the wire 23.5A

Part B

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

Please enter your answer as two distances, the first distance from the wire carrying 23.5A, and the second distance from the wire carrying 77.5A seperate the values with a comma

Explanation / Answer

Part A)

If the currents are in the same direction, there will be only one location, and that will be between the wires

The formula that governs this is B = uI/2pir and the two B's will need to equal each other

Thus uI/2pir = uI/2pir   -- u and 2pi will cancel, so...

I/r = I/r

23.5/x = 77.5/(35 - x) -- Cross Multiply

822.5 - 23.5x = 77.5x

822.5 = 101x

x = 8.14 cm from the 23.5 A wire

Part B)

When the currents are in opposite directions, the location will be on the opposite side of the 23.5 A wire

23.5/x = 77.5(35 + x)

822.5 + 23.5x = 77.5 x

822.5 = 54x

x = 15.2 cm away from the 23.5 A wire

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