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Two long parallel transmission lines 39.5cm apart carry 30.0A and 72.0A currents.

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

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

Please, answer as two distances, the first distance from the wire carrying 30.0A , and the second distance from the wire carrying 72.0A . Separate the values with a comma.
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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 30 A and in between 30 A and 72 A carrying wire.

this gives

mU * o*30/(2*pi*x) =  \muo*72/(2*pi*39.5-x)

30/x = 72/(39.5-x)

30*(39.5-x) = 72x

1185 - 30x = 72x

102x = 1185

x = 11.61 cm

therefore magnetic field is zero at 11.61 cm from 30 A carrying wire and in between two wires

When currents are in opposite direction

Mu * o*30/(2*pi*x) = - mU * o*72/(2*pi*39.5-x)

30/x = -72/(39.5-x)

1185 - 30x = -72x

1185 = -42x

x = 28.21 cm

therefore, magnetic feild is zero at point 28.21 cm from 30 A carrying wire

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