Q123 / 150 · MHT CET 2024 (09 May Shift 2) · Physics
A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. $I_c$ and $I_w$ are the currents through circular loop and long straight wire respectively. The perpendicular distance between centre of the circular loop and wire is ' $d$ '. The magnetic field at the centre of the loop will be zero when separation ' $d$ ' is equal to
- Correct answerA$\frac{R I_w}{\pi I_c}$
- B$\frac{R I_{\mathrm{e}}}{\pi \mathrm{I}_{\mathrm{w}}}$
- C$\frac{\pi \mathrm{I}_{\mathrm{c}}}{\mathrm{RI}_{\mathrm{w}}}$
- D$\frac{\pi \mathrm{I}_{\mathrm{w}}}{\mathrm{R}_{\mathrm{c}}}$
Solution
For magnetic field to be zero at centre of loop, Magnetic field due to circular loop = Magnetic field due to current carrying wire
$\begin{array}{ll}
& \frac{\mu_0 I_c}{2 R}=\frac{\mu_0 I_w}{2 \pi d} \\
\therefore \quad & d=\frac{R I_w}{\pi I_c}
\end{array}$
Hence, the correct answer is option: 'A'.