Q176 / 180 · KCET 2010 · Physics
$\mathrm{PQ}$ 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 2 A is switched off. The field at $M$ now becomes
- A$2 \mathrm{~B}$
- Correct answerB$\mathrm{B}$
- C$\frac{\mathrm{B}}{2}$
- D$3 B$
Solution
Magnetic field at midpoint $M$ in first case is
$$
\mathrm{B}=\mathrm{B}_{\mathrm{PQ}}-\mathrm{B}_{\mathrm{RS}}
$$
$\left(\because \mathrm{B}_{\mathrm{PQ}}\right.$ and $\mathrm{B}_{\mathrm{RS}}$ are in opposite directions)
$$
\begin{aligned}
&=\frac{4 \mu_{0}}{4 \pi \mathrm{d}}-\frac{2 \mu_{0}}{4 \pi \mathrm{d}} \\
&=\frac{2 \mu_{0}}{4 \pi \mathrm{d}}
\end{aligned}
$$
When the current $2 \mathrm{~A}$ is switched off, the net magnetic field at $\mathrm{M}$ is due to current $1 \mathrm{~A}$
$$
\mathrm{B}^{\prime}=\frac{\mu_{0} \times 2 \times 1}{4 \pi \mathrm{d}}=\mathrm{B}
$$
Hence, the correct answer is option: 'B'.