A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the…

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
  1. $\frac{R I_w}{\pi I_c}$
  2. $\frac{R I_{\mathrm{e}}}{\pi \mathrm{I}_{\mathrm{w}}}$
  3. $\frac{\pi \mathrm{I}_{\mathrm{c}}}{\mathrm{RI}_{\mathrm{w}}}$
  4. $\frac{\pi \mathrm{I}_{\mathrm{w}}}{\mathrm{R}_{\mathrm{c}}}$

Solution

For magnetic field to be zero at centre of loop, Magnetic field due to circular loop = Magnetic field due to current carrying wire $\begin{array}{ll} & \frac{\mu_0 I_c}{2 R}=\frac{\mu_0 I_w}{2 \pi d} \\ \therefore \quad & d=\frac{R I_w}{\pi I_c} \end{array}$

Asked in: MHT CET 2024 (09 May Shift 2)

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