Name: Factors Affecting Magnetic Field of Straight Wire
Uploaded: 2019-07-19
Duration: 4 min 9 s
Description: We know a magnetic field is produced by current flowing in a straight conductor. In this video, let us learn the different factors affecting the intensity of...

Question

Find out the expression for the magnetic field at a point on the axis of a toroid of

N

turns having an average radius

r

and carrying a current

I

. Show that the magnetic field at the open space inside and outside the toroid is zero.

Accepted Answer

The toroid is a hollow circular ring on which a large number of turns of a wire are closely wound.
Consider a sectional view of the toroid. The direction of the magnetic field inside is clockwise as per the right-hand thumb rule for circular loops. Consider Three circular Amperian loops 1, 2 and 3 are shown by dashed lines. The magnetic field is tangential to the given loop.

Let the magnetic field inside the toroid be $B$ . Then by Ampere's circuital law,

$\oint B . dl = μ_{0} I or BL = μ_{0} NI$ where $N$ = number of turns, and $μ_{0}$ = permeability of free space.

Since the length of a loop $L = 2 πr$ ( $r$ = radius of a loop)
Where $L$ is the length of the loop for which $B$ is tangential, $I$ is the current enclosed by one loop
Therefore, we have,

$B (2 πr) = μ NI or B = \frac{μNI}{2 πr}$ ...............................................(A)

Open space inside the toroid encloses no current thus, $I = 0$ Hence, $B = 0$ .......(B)
Open space exterior to the toroid :
Each turn of current-carrying wire is cut twice by the loop $3$ . Thus, the current coming out of the plane of the paper is cancelled exactly by the current going into it.

Hence, $I = 0 thus B = 0$ ..................................(C)

Find out the expression for the magnetic field at a point on the axis of a toroid of $N$ turns having an average radius $r$ and carrying a current $I$ . Show that the magnetic field at the open space inside and outside the toroid is zero.

Important Questions on Electromagnetism

Learn and Prepare for any exam you want !

Find out the expression for the magnetic field at a point on the axis of a toroid of N turns having an average radius r and carrying a current I. Show that the magnetic field at the open space inside and outside the toroid is zero.

Important Questions on Electromagnetism

Learn and Prepare for any exam you want !

Find out the expression for the magnetic field at a point on the axis of a toroid of $N$ turns having an average radius $r$ and carrying a current $I$ . Show that the magnetic field at the open space inside and outside the toroid is zero.