A toroid with thick windings of $N$ turns has inner and outer radii $R_{1}$ and $R_{2}$, respectively. If it carries certain steady current $I$, the variation of the magnetic field due to the toroid with radial distance is correctly graphed in

• A

  
  
  
• B

  
  
  
• C

  
  
  
• Correct answer
  D

  
  
  

Solution

Magnetic field due to toroid can be given as (i) In the open space, cxtcrior of a toroid, $B=0$

(ii) Inside the toroid, $B=\frac{\mu_{0} N I}{2 \pi r}$ Here, $r=\frac{R_{1}+R_{2}}{2}$ $\Rightarrow \quad B=\frac{\mu_{0} N I}{\pi\left(R_{1}+R_{2}\right)}=$ constant So, the variations of $B$ with $r$ is correctly depicted in option (d). in option (d).

Hence, the correct answer is option: 'D'.