Answer:
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;
[tex]B = \frac{\mu I}{2\pi d }[/tex]
where;
B is the magnetic field
when the current is 30 A, the magnetic field midway between the wires
[tex]B_1 = \frac{30*\mu}{2\pi d/2} = \frac{30*\mu}{\pi d}[/tex]
when the current is increased to 50 A, the magnetic field midway between the wires;
[tex]B_2 = \frac{50* \mu}{2\pi d/2} = \frac{50* \mu}{\pi d}[/tex]
the magnitude of the magnetic field midway between the wires changes by a factor of;
[tex]\frac{B_2}{B_1} = \frac{50*\mu}{\pi d} X \frac{\pi d}{30*\mu} \\\\\frac{B_2}{B_1} = \frac{50}{30} = 1.67 = 167 \%[/tex]
Thus, the magnitude of the magnetic field midway between the wires increased by a factor of ²/₃ or 67%.
