Question

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?

Answer 1

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

Step-by-step 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;

`B = (\mu I)/(2\pi d )`

where;

B is the magnetic field

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

`B_1 = (30*\mu)/(2\pi d/2) = (30*\mu)/(\pi d)`

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

`B_2 = (50* \mu)/(2\pi d/2) = (50* \mu)/(\pi d)`

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

`(B_2)/(B_1) = (50*\mu)/(\pi d) X (\pi d)/(30*\mu) \\\\(B_2)/(B_1) = (50)/(30) = 1.67 = 167 \%`

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