Question

Toroid has 4900 turns, \( I = 12\ \text{A} \), average radius = \( 24.5\ \text{cm} \). Find magnetic field inside core.

• A. 56 mT
• B. 54 mT
• C. 42 mT
• D. 48 mT

Hint:

Use \( B = \frac{\mu_0 N I}{2\pi r} \) for toroid, where \( r \) is average radius.

Answer 1

The Correct Option is D

Magnetic field in toroid: \[ B = \frac{\mu_0 N I}{2\pi r} \] \[ \mu_0 = 4\pi \times 10^{-7},\ N = 4900,\ I = 12,\ r = 0.245\ \text{m} \] \[ B = \frac{4\pi \cdot 4900 \cdot 12 \cdot 10^{-7}}{2\pi \cdot 0.245} = \frac{4 \cdot 4900 \cdot 12 \cdot 10^{-7}}{2 \cdot 0.245} = \frac{235200 \cdot 10^{-7}}{0.49} = 48 \times 10^{-3} = 48\ \text{mT} \]