An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current I…

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current I ampere and the radius of the circular loop is r metre. Then the magnetic induction B at the centre of the circular part is:
  1. zero
  2. infty
  3. \(\frac{\mu_{\mathrm{o}} 2 \mathrm{I}}{4 \pi \mathrm{r}}(\pi+1)\)
  4. \(\frac{\mu_{\mathrm{o}}}{4 \pi} \times \frac{2 \mathrm{I}}{\mathrm{R}}(\pi-1)\)

Solution

$\begin{aligned} & B=\left|\frac{\mu_{\mathrm{OI}}}{2 \pi R}-\frac{\mu_{\mathrm{OI}}}{2 R}\right| \\ & B=\frac{\mu_{\mathrm{OI}}}{2 R}\left(1-\frac{1}{11}\right) \\ & =\frac{\mu_{\mathrm{OI}}}{2 \pi R}(\pi-1) \\ & =\frac{\mu_{\mathrm{OI}}}{4 \pi} \times \frac{2 I}{R}(\pi-1) \end{aligned}$ $\therefore$ Option D is the correct answer.

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

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