SATHEE: moving-charges-and-magnetism Question 32

moving-charges-and-magnetism Question 32

Question: Q. 7. (i) How is a toroid different from a solenoid ?

(ii) Use Ampere’s circuital law to obtain the magnetic field inside a toroid.

(iii) Show that in an ideal toroid, the magnetic field (a) inside the toroid and (b) outside the toroid at any point in the open space is zero.

U] [O.D. Comptt. I, II, III 2014]

Show Answer

Solution:

Ans. (i) A toroid can be viewed as a solenoid which has been bent into a circular shape to close on itself. 1 (ii)

For the magnetic field at a point $S$ inside a toroid we have

$\begin{aligned} B (2 π r) & = μ_{0} N I B & = μ_{0} \frac{N I}{2 π r} = μ_{0} n I \end{aligned}$

( $n =$ no. of turns per unit length of solenoid) $1 / 2$

$n = \frac{N}{2 π r}$

(iii) For the loop 1, Ampere’s circuital law gives $B_{1} .2 π r_{1} = μ_{0} (0)$ , i.e. $B_{1} = 0$

Thus the magnetic field, in the open space inside the toroid is zero

Also at point $Q$ , we have $B_{3} (2 π r_{3}) = μ_{0} (I_{enclosed})$ But from the section cut, we see that the current coming out of the plane of the paper, is cancelled exactly by the current going into it.

Hence,

$I_{enclosed} = 0$

$B_{3} = 0$

$1 / 2$

[CBSE Marking Scheme 2014]

Answering Tips

Practice the derivation of Ampere’s Circuital Law to obtain the magnetic field inside a toroid.

Moving Charges And Magnetism

moving-charges-and-magnetism Question 32

Answering Tips

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Moving Charges And Magnetism

moving-charges-and-magnetism Question 32

Answering Tips

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu