First slide

Magnetic field due to a current carrying circular ring

Question

The magnetic field at the centre of a circular coil of radius r and carrying a current i is B. What is the magnetic field at a distance $X = \sqrt{3} r$ r from the centre, on the axis of the coil ?

Moderate

A

B
B

B/2
C

B/4
D

B/8

Solution

The magnetic induction at the centre of circular coil is given by
$B = B_{0} = \frac{μ_{0} Ni}{2 r}$ ………………….(1)
The magnetic' induction at a distance x on the axis of circular coil is given by
$\begin{array}{l} B_{X} = \frac{μ_{0} {Nir}^{2}}{2 (r^{2} + x^{2} j^{3 / 2}} \\ = \frac{μ_{0} {Nir}^{2}}{2 {(r^{2} + 3 r^{2})}^{3 / 2}} (∵ x = \sqrt{3} r) \end{array}$
$= \frac{μ_{0} {Nir}^{2}}{16 r^{3}} = \frac{μ_{0} Ni}{16 r}$ …………….(2)
From eqs. (1) and (2), B_x = B / 8

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App