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. The current through circular loop and long straight wire are ' $I_C$ ' and ' 1 w ' 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. $\frac{\mathrm{RI}_{\mathrm{w}}}{\pi \mathrm{I}_{\mathrm{C}}}$
  2. $\frac{R I_C}{\pi I_w}$
  3. $\frac{\pi \mathrm{I}_{\mathrm{C}}}{\mathrm{RI}_{\mathrm{w}}}$
  4. $\frac{\pi \mathrm{I}_{\mathrm{w}}}{\mathrm{RI}_{\mathrm{C}}}$

Solution

Magnetic field due to straight wire $=\frac{\mu_0 I_w}{2 \pi d}$ Magnetic field due to circular loop $=\frac{\mu_0 I_C}{2 R}$ As magnetic field at centre is zero $\begin{array}{ll} & \frac{\mu_0 I_w}{2 \pi d}=\frac{\mu_0 I_c}{2 R} \\ \therefore \quad & d=\frac{R I_w}{\pi I_c} \end{array}$

Asked in: MHT CET 2024 (11 May Shift 2)

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