Question:
A toroid of \(1000\) turns has average radius
\[
\frac{\mu_0}{\pi}\ \text{metre}.
\]
If a current of \(1\,A\) is flowing through it, then the magnetic field intensity inside the coil of the toroid is
A toroid of \(1000\) turns has average radius
\[
\frac{\mu_0}{\pi}\ \text{metre}.
\]
If a current of \(1\,A\) is flowing through it, then the magnetic field intensity inside the coil of the toroid is
Show Hint
For a toroid,
\[
B=\frac{\mu_0NI}{2\pi r}.
\]
The magnetic field is directly proportional to the number of turns and current, and inversely proportional to the mean radius.
Updated On: Jul 29, 2026
- \(500\,T\)
- \(100\,T\)
- \(750\,T\)
- \(1000\,T\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
The magnetic field inside a toroid is
\[
B=\frac{\mu_0NI}{2\pi r},
\]
where
\[
N=\text{number of turns},
\quad
I=\text{current},
\quad
r=\text{mean radius of the toroid}.
\]
Step 1: Write the given data. \[ N=1000, \qquad I=1\,A, \qquad r=\frac{\mu_0}{\pi}. \]
Step 2: Substitute into the toroid field formula. \[ B = \frac{\mu_0(1000)(1)} {2\pi\left(\frac{\mu_0}{\pi}\right)}. \] \[ = \frac{1000\mu_0} {2\mu_0}. \] \[ = 500. \] Hence, \[ B=500\,T. \]
Step 3: Identify the correct option. \[ \boxed{B=500\,T} \] Therefore, \[ \boxed{\text{Answer = (A)}} \]
Step 1: Write the given data. \[ N=1000, \qquad I=1\,A, \qquad r=\frac{\mu_0}{\pi}. \]
Step 2: Substitute into the toroid field formula. \[ B = \frac{\mu_0(1000)(1)} {2\pi\left(\frac{\mu_0}{\pi}\right)}. \] \[ = \frac{1000\mu_0} {2\mu_0}. \] \[ = 500. \] Hence, \[ B=500\,T. \]
Step 3: Identify the correct option. \[ \boxed{B=500\,T} \] Therefore, \[ \boxed{\text{Answer = (A)}} \]
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