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
$B=B_{P Q}-B_{R S}$
$\left(\because B_{P Q}\right.$ and $B_{R S}$ 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 $2 A$ is switched off, the net magnetic field at $M$ is due to current $1 A$
$B'=\frac{\mu_{0} \times 2 \times 1}{4 \pi d}=B$