Toroid - Practice Questions & MCQ

Toroid -

If we try to bend a solenoid in the form of a ring then the obtained shape is a Toroid. So, a toroid can be considered a ring-shaped closed solenoid. Hence it is like an endless cylindrical solenoid. From the given figure we can understand Toroid much better.

Now to obtain the magnetic field by a toroid, let us consider a toroid having N turns.

Here, we will now apply Ampere circuital law to calculate the magnetic field of a toroid. Suppose we have to find the magnetic field B at a point P inside the toroid as shown below in figure - 

Let us take an amperian loop which is a circle through point P and concentric inside the toroid. By symmetry, field will have equal magnitude at all points of this circle and this field is tangential to every point in the circle
Thus, 

                                                                          $\begin{aligned} & \oint B \cdot d l=\mu_0 \mathrm{NI} \\ & \text { or, } \\ & 2 \pi r \mathrm{~B}=\mu_0 \mathrm{NI} \\ & \text { or, } \\ & \mathrm{B}=\frac{\mu_0 \mathrm{NI}}{2 \pi r}\end{aligned}$

From the above result, B varies with r i.e. field B is not uniform over the cross-section of the core because as we increase 'r' the B varies.