JEE Main Maths Syllabus 2025 - Download JEE Mathematics Topics Wise Syllabus PDF

# Toroid - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• 4 Questions around this concept.

## Solve by difficulty

A toroidal solenoid has 3000 turns and a mean radius of 10 cm. It has a soft iron core of relative permeability 2000. What is the magnitude of the magnetic field in the core when a current of 1 A is passed through the solenoid?

A loosely wound helix made of stiff wire is mounted vertically with the lower end just touching a dish of mercury. When a current from the battery is started in the coil through the mercury :

A toroid of mean radius ' a ', cross-section radius ' r ' and a total number of turns N. it carries a current ' i '. The torque experienced by the toroid if a uniform magnetic field of strength  B  is applied.

## Concepts Covered - 1

Toroid

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,

$\begin{array}{l}{\oint B . d l=\mu_{0} \mathrm{NI}} \\ {\text { or, }} \\ \\ {2 \pi r \mathrm{B}=\mu_{0} \mathrm{NI}} \\ {\text { or, }} \\ \\ {\mathrm{B}=\frac{\mu_{0} \mathrm{NI}}{2 \pi r}}\end{array}$

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.

## Study it with Videos

Toroid

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