Advertisement Remove all ads

Use this Law to Obtain the Expression for the Magnetic Field Inside an Air Cored Toroid of Average Radius 'r', Having 'n' Turns per Unit Length and Carrying a Steady Current I. - Physics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius 'r', having 'n' turns per unit length and carrying a steady current I.

Advertisement Remove all ads


A toroid is a hollow circular ring on which a large number of turns of a wire are closely wound. Consider an air-cored toroid (as shown above) with centre O.

r = Average radius of the toroid
I = Current through the solenoid
n = Number of turns per unit length

To determine the magnetic field inside the toroid, we consider three amperian loops (loop 1, loop 2 and loop 3) as show in the figure below.

For loop 1:

According to Ampere's circuital law, we have


Total current for loop 1 is zero because no current is passing through this loop.

So, for loop 1


For loop 3:

According to Ampere's circuital law, we have


Total current for loop 3 is zero because net current coming out of this loop is equal to the net current going inside the loop.

For loop 2:

The total current flowing through the toroid is NI, where N is the total number of turns.


Now, `vecB `



Comparing (i) and (ii), we get



 Number of turns per unit length is given by



This is the expression for magnetic field inside air-cored toroid.

Concept: Solenoid and the Toroid - the Solenoid
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×