Two long parallel wires are a distance d apart. The current in one wire is 10 A and the current in the other wire is 30 A. The currents are in the same direction. If the 30-A current is increased to 50 A, by what factor does the magnitude of the magnetic field midway between the wires change?

The magnitude of the magnetic field midway between the wires increased by a factor of  ²/₃ or 67%.

Explanation:

Given;

current in the first wire, I₁ = 10 A

current in the second wire, I₂ = 30 A

magnetic filed produced in the first wire due to the current in the second wire is given as;

where;

B is the magnetic field

when the current is 30 A, the magnetic field midway between the wires

when the current is increased to 50 A, the magnetic field midway between the wires;

the magnitude of the magnetic field midway between the wires changes by a factor of;

Thus, the magnitude of the magnetic field midway between the wires increased by a factor of ²/₃ or 67%.

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