Two parallel long wires carry currents $i_{1}$ and $i_{2}$ and ( $i_{1}i_{2}$ ). When the currents

Question

Two parallel long wires carry currents $i_{1}$ and $i_{2}$ and ( $i_{1}>i_{2}$ ). When the currents are in the same direction, the magnetic induced at a point midway between the two wires is $x$. If the direction of $i_{2}$ is reversed, the magnetic induction becomes $4 x$. Then ( $\mathrm{i}_{1} / \mathrm{i}_{2}$ ) is\

Professor PC Thomas Classes · Answer

\ $\mathrm{B}^{\prime}=\mathrm{B}_{1}+\mathrm{B}_{2}=\frac{\mu_{0}}{2 \pi \mathrm{r} / 2}\left(\mathrm{I}_{1}+\mathrm{I}_{1}ight)=4 \mathrm{x}$\ $\frac{\mathrm{B}}{\mathrm{B}^{\prime}}=\frac{\mathrm{I}_{1}-\mathrm{I}_{2}}{\mathrm{I}_{1}+\mathrm{I}_{2}}=\frac{1}{4}, 4 \mathrm{I}_{1}-4 \mathrm{I}_{2}=\mathrm{I}_{1}+\mathrm{I}_{2}$\ $3 \mathrm{I}_{1}=5 \mathrm{I}_{2}$\ $\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{5}{3}$\