Question

The magnetic field (in $10^{-4}$ T) at the centre of a toroid of mean radius 10 cm with 200 turns and carrying a current of 2.5 A is:

• A. $2\pi$
• B. 10
• C. 5
• D. Zero

Hint:

Magnetic field inside a toroid: $B = \mu_0 N I/(2 \pi r)$.
Convert T to $10^{-4}$ T for matching options.
Check units carefully.

Answer 1

The Correct Option is A

• Magnetic field inside toroid: $B = \dfrac{\mu_0 N I}{2\pi r}$.
• $r = 0.1$ m, $N = 200$, $I = 2.5$ A, $\mu_0 = 4\pi\times10^{-7}$ T·m/A.
• $B = \dfrac{4\pi \cdot 10^{-7} \cdot 200 \cdot 2.5}{2\pi \cdot 0.1} = 2\times10^{-3}\ \text{T} = 2\pi \cdot 10^{-4}$ T.
• Hence correct answer: $2\pi$ in $10^{-4$ T units}.