Two long parallel transmission lines 39.0 cm apart carry 20.5 A and 72.5 A curre

Question

Two long parallel transmission lines 39.0 cm apart carry 20.5 A and 72.5 A currents.

Part A Find all locations 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 carrying 20.5 A . x = m cm

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 20.5 A , and the second distance from the wire carrying 72.5 A . Separate the values with a comma.

Explanation / Answer

magnetic field due to current carrying wire = mU * o*I/(2*pi*r)

let the point be at the distance of x from wire carrying 20.5 A and in between 30 A and 72.5 A carrying wire.

this gives

mU * o*20.5/(2*pi*x) = muo*72.5/(2*pi*39.0-x)

20.5/x = 72.5/(39.0-x)

20.5*(39.0-x) = 72.5x

799.5 - 20.5x = 72.5x

93x = 799.5

x = 8.59 cm

therefore magnetic field is zero at 8.59 cm from 20.5 A carrying wire and in between two wires

When currents are in opposite direction

Mu * o*20.5/(2*pi*x) = - mU * o*72.5/(2*pi*39.0-x)

20.5/x = -72.5/(39.0-x)

799.5 - 20.5x = -72.5x

799.5 = -52x

x = 15.375 cm

therefore, magnetic feild is zero at point 15.375 cm from 20.5 A carrying wire

and 28.21 + 39.5 = 67.71 cm from 72 A carrying wire

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