First slide

Magnetic field due to a current carrying circular ring

Question

The magnetic induction at the centre O in the figure shown is

Moderate

A

$\frac{μ_{0} i}{4} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
B

$\frac{μ_{0} i}{4} (\frac{1}{R_{1}} + \frac{1}{R_{2}})$
C

$\frac{μ_{0} i}{4} (R_{1} - R_{2})$
D

$\frac{μ_{0} i}{4} (R_{1} + R_{2})$

Solution

In the following figure, magnetic fields at O due to sections 1, 2, 3 and 4 are considered as B₁ , B₂, B₃ and B₄, respectively.
B₁ = B₃ = 0
$\begin{array}{l} B_{2} = \frac{μ_{0}}{4 π} . \frac{π}{R_{1}} \otimes \\ B_{4} = \frac{μ_{0}}{4 π} . \frac{πi}{R_{2}} ⊙ \\ As |B_{2}| > |B_{4}| \\ So B_{net} = B_{2} - B_{4} \Rightarrow B_{net} = \frac{μ_{0} i}{4} (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \otimes \end{array}$

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