HSC Science (General) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Obtain an Expression for Magnetic Induction Along the Axis of Toroid. - HSC Science (General) 12th Board Exam - Physics

Login
Create free account


      Forgot password?

Question

Obtain an expression for magnetic induction along the axis of the toroid.

Solution

Magnetic induction along the axis of toroid:

The toroid is a solenoid bent into a shape of the hollow doughnut.

Consider a toroidal solenoid of average radius ‘r’ having center carrying the current I. In order to find magnetic field produced at the center along the axis of toroid due to the current flowing through the coil, imagine an Amperial loop of radius ‘r’ and traverse it in the clockwise direction.

According to Ampere’s circuital law, 

`ointvecB.vec(dL)=mu_0I`

Here current I flow through the ring as many times time as there are the number of turns. Thus the total current flowing through toroid is N I , where N is the total number of turns.

`:.ointvecB.vec(dL)=mu_0NI" ---------(1)"`

Now, and are in same direction `:.ointvecB.vec(dL)=BointdL`

`:.ointvecB.vec(dL)=B(2pir)" ------(2)"`

Comparing equation (1) and equation (2 )

μ0NI=B(2πr)  `:.B=(mu_0NI)/(2pir)` .......(3)

If ‘n’ is the number of turns per unit length of toroid then `n=N/(2pir)`

Substituting this value in equation No (3) we get B = μ0 n I

  Is there an error in this question or solution?

APPEARS IN

 2013-2014 (March) (with solutions)
Question 6.1 | 3.00 marks
 2016-2017 (July) (with solutions)
Question 6.2 | 3.00 marks

Video TutorialsVIEW ALL [2]

Solution Obtain an Expression for Magnetic Induction Along the Axis of Toroid. Concept: Ampere’s Circuital Law.
S
View in app×