Question-11 Two identical long parallel wires carry currents I_1 and I_2 such that I_1>I_2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 8\times10^{-6}\ T. If the direction of I_2 is reversed, the field becomes 3.2\times10^{-5}\ T. The ratio of I_2 to I_1 is
(A) 1:4
(B) 2:5
(C) 3:5
(D) 3:4
Answer : (C)
Explanation:
When the currents are in the same direction
B=B_1-B_2 8\times10^{-6}=\frac{\mu_0 I_1}{2\pi r}-\frac{\mu_0 I_2}{2\pi r}∴ \frac{\mu_0}{2\pi r}(I_1-I_2)=8\times10^{-6} ….(i)
When the current flows in opposite direction,
B=B_1+B_2∴ \frac{\mu_0}{2\pi r}(I_1+I_2)=3.2\times10^{-5} ….(ii)
Dividing equation (i) by (ii), we get,
\frac{I_1-I_2}{I_1+I_2}=\frac{8\times10^{-6}}{3.2\times10^{-5}}=0.25 I_1-I_2=(0.25)(I_1+I_2) 0.75 I_1=1.25 I_2∴ \frac{I_2}{I_1}=\frac{0.75}{1.25}=\frac{3}{5}