MHT CET · Physics · Magnetic Effects of Current
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
- A \(\frac{R I_w}{\pi I_c}\)
- B \(\frac{R I_{\mathrm{e}}}{\pi \mathrm{I}_{\mathrm{w}}}\)
- C \(\frac{\pi \mathrm{I}_{\mathrm{c}}}{\mathrm{RI}_{\mathrm{w}}}\)
- D \(\frac{\pi \mathrm{I}_{\mathrm{w}}}{\mathrm{R}_{\mathrm{c}}}\)
Answer & Solution
Correct Answer
(A) \(\frac{R I_w}{\pi I_c}\)
Step-by-step Solution
Detailed explanation
For magnetic field to be zero at centre of loop, Magnetic field due to circular loop = Magnetic field due to current carrying wire
\(\begin{array}{ll}
& \frac{\mu_0 I_c}{2 R}=\frac{\mu_0 I_w}{2 \pi d} \\
\therefore \quad & d=\frac{R I_w}{\pi I_c}
\end{array}\)
\(\begin{array}{ll}
& \frac{\mu_0 I_c}{2 R}=\frac{\mu_0 I_w}{2 \pi d} \\
\therefore \quad & d=\frac{R I_w}{\pi I_c}
\end{array}\)
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