A toroid has a non-ferromagnetic wire of inner radius ' $\mathrm{r}_{1}{ }^{\prime}$ and outer radius '…

A toroid has a non-ferromagnetic wire of inner radius ' $\mathrm{r}_{1}{ }^{\prime}$ and outer radius ' $\mathrm{r}_{2}$ ', around which 'N' turns of wire are wound. If the current in the wire is ' $\mathrm{I}^{\prime}$, then the magnetic field inside the toroid is $\left(\mu_{0}=\right.$ permeability of free space $)$
  1. $\frac{\mu_{0} \mathrm{NI}}{\pi\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}$
  2. $\frac{\mu_{0} \mathrm{NI}}{\left(\mathrm{r}_{2}-\mathrm{r}_{1}\right)}$
  3. $\frac{\mu_{0} \mathrm{NI}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}$
  4. $\frac{\mu_{0} \mathrm{NI}}{\pi\left(\mathrm{r}_{2}-\mathrm{r}_{1}\right)}$

Solution

$\begin{aligned} r &=\frac{r_{1}+r_{2}}{2} \\ B &=n \mu_{0} I=\mu_{0} I \frac{N}{2 \pi r}=\frac{\mu_{0} I N \times 2}{2 \pi\left(r_{1}+r_{2}\right)} \\ &=\frac{\mu_{0} I N}{\pi\left(r_{1}+r_{2}\right)} \end{aligned}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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