Question

$PQ$ and $RS$ are long parallel conductors separated by certain distance. $M$ is the midpoint between them (see the figure). The net magnetic field at $M$ is $B$. Now, the current $2A$ is switched off. The field at $M$ now becomes............

• A. $\frac{B}{2}$
• B. $3B$
• C. $2B$
• D. $B$

Answer 1

Answer: (D)

Magnetic field at midpoint $M$ in first case is
$B=B_{PQ}-B_{RS}$
$(\because B_{PQ}$ and $B_{RS}$ are in opposite directions)
$=\frac{4{\mu }_0}{4\pi d}-\frac{2{\mu }_0}{4\pi d}$
$=\frac{2{\mu }_0}{4\pi d}$
When the current $2A$ is switched off, the net magnetic field at $M$ is due to current $1A$
$B^{\prime }=\frac{{\mu }_0\times 2\times 1}{4\pi d}=B$