Question

hello why is boutside 0 for torioid

Answer 1

The magnetic field outside a toroid is zero.

Answer 2

The magnetic field outside a toroid is zero due to Ampere's Law. Ampere's Law states that the line integral of the magnetic field $\vec{B}$ around a closed loop is equal to $\mu_0$ times the total current $I_{enc}$ enclosed by the loop: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$ To find the magnetic field outside a toroid, we consider an Amperian loop that is a circle concentric with the toroid's axis and located outside the toroid. The toroid's windings pass through the area enclosed by this loop. However, for every turn where the current enters the area enclosed by the loop, there is an equal number of turns where the current exits. Consequently, the net current $I_{enc}$ enclosed by such an outer loop is zero. Applying Ampere's Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 (0) = 0$ By symmetry, the magnetic field $\vec{B}$ must be tangential to the Amperian loop and have a constant magnitude along it. For the integral to be zero, the magnetic field $\vec{B}$ must be zero everywhere outside the toroid.