Question

The magnetic field at a point midway between two parallel long wires carrying currents in the same direction is $10\mu T$. If the direction of the smaller current among them is reversed, the field becomes $30\mu T$. The ratio of the larger to the smaller current in them is

• A. 3 : 1
• B. 2 : 1
• C. 4 : 1
• D. 3 : 2
• E. 3 : 4

Answer 1

The correct option is B 2 : 1

By Ampere's law, the magnetic field at a distance d from the long wire is $B=\frac{{\mu }_{0}I}{2\pi d}$

When the current in same direction, the net magnetic field between the wires is

$B=\frac{{\mu }_{0}I}{2\pi d}(I_2-I_1)=10\mu T$

When small current $I_1$ (say) direction is reversed, the net magnetic field between the wires will be

$B^{\prime }=\frac{{\mu }_{0}I}{2\pi d}(I_2+I_1)=30\mu T$

So, $\frac{I_2-I_1}{I_1+I_2}=\frac{10}{30}$

or $3I_2-3I_1=I_1+I_2$

or $2I_2=4I_1$

or $I_2/I_1=2/1$