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MHT CET · Physics · Magnetic Effects of Current

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. A \(\frac{\mu_{0} \mathrm{NI}}{\pi\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}\)
  2. B \(\frac{\mu_{0} \mathrm{NI}}{\left(\mathrm{r}_{2}-\mathrm{r}_{1}\right)}\)
  3. C \(\frac{\mu_{0} \mathrm{NI}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}\)
  4. D \(\frac{\mu_{0} \mathrm{NI}}{\pi\left(\mathrm{r}_{2}-\mathrm{r}_{1}\right)}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mu_{0} \mathrm{NI}}{\pi\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}\)

Step-by-step Solution

Detailed explanation

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