Concept:A toroid can be thought of as a solenoid bent into a circular donut shape. The magnetic field inside the core of a toroid is found using Ampere's Law.
Formula:$$ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}} $$
Solution:- Choose a circular Amperian loop of radius \( r \) strictly inside the toroidal core. The length of this loop is \( 2\pi r \).
- If there are \( N \) total turns of wire, the total enclosed current is \( NI \).
- Applying Ampere's law gives: \( B(2\pi r) = \mu_0 NI \).
- Rearranging for \( B \) gives: \( B = \frac{\mu_0 NI}{2\pi r} \).
Why other options are incorrect:Option A is the formula for the interior of a straight, infinitely long solenoid using turn density \( n \), not total turns \( N \). Options C and D are dimensionally incorrect.
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