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(C) Let the distance of the midpoint from each wire be $r$. The magnetic field due to a long straight wire at a distance $r$ is given by $B = \frac{\m

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$B$

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(C) Let the distance of the midpoint from each wire be $r$. The magnetic field due to a long straight wire at a distance $r$ is given by $B = \frac{\mu_0 I}{2\pi r}$.According to the right-hand rule,the magnetic field due to the wire with current $I$ at the midpoint points into the page,and the field due to the wire with current $2I$ points out of the page.The net magnetic field $B$ at the midpoint is the difference between the magnitudes of the two fields:$B = \left| \frac{\mu_0 (2I)}{2\pi r} - \frac{\mu_0 I}{2\pi r} \right| = \frac{\mu_0 I}{2\pi r}$.When the wire carrying current $2I$ is switched off,the remaining magnetic field at the midpoint is due only to the wire carrying current $I$:$B' = \frac{\mu_0 I}{2\pi r}$.Comparing the two expressions,we see that $B' = B$.

$A$ wire carrying current $I$ and another carrying $2I$ in the same direction produce a magnetic field $B$ at the midpoint. What will be the field when the $2I$ wire is switched off?

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