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Question

(D) Let the distance between the wires be $2r$. The distance from each wire to the midpoint is $r$. The magnetic field due to a long wire at distance

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(D) Let the distance between the wires be $2r$. The distance from each wire to the midpoint is $r$. The magnetic field due to a long wire at distance $r$ is $B = \frac{\mu_0 I}{2 \pi r}$.When currents are in the same direction,the fields at the midpoint are in opposite directions. The net field is $B_1 = \frac{\mu_0}{2 \pi r} (I_1 - I_2) = 6 	imes 10^{-6} \ T$.When the direction of $I_2$ is reversed,the fields at the midpoint are in the same direction. The net field is $B_2 = \frac{\mu_0}{2 \pi r} (I_1 + I_2) = 3 	imes 10^{-5} \ T$.Dividing the two equations: $\frac{I_1 - I_2}{I_1 + I_2} = \frac{6 	imes 10^{-6}}{3 	imes 10^{-5}} = \frac{6}{30} = \frac{1}{5}$.$5(I_1 - I_2) = I_1 + I_2 \implies 5I_1 - 5I_2 = I_1 + I_2 \implies 4I_1 = 6I_2$.Therefore,$\frac{I_1}{I_2} = \frac{6}{4} = \frac{3}{2}$.

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