First slide

Magnetic field due to a current carrying circular ring

Question

A wire is bent in the form of a circular arc with a straight portion AB. Magnetic induction at O when current I is flowing in the wire, is

Moderate

A

$\frac{μ_{0}}{2 r} (π - θ + tanθ)$
B

$\frac{μ_{0}}{2 πr} (π + θ - tanθ)$
C

$\frac{μ_{0} I}{2 πr} (π - θ + tanθ)$
D

$\frac{μ_{0} I}{2 πr} (- tanθ + π - θ)$

Solution

$\begin{array}{l} B_{AB} = \frac{μ_{0} I}{4 π (OC)} [2 \sin θ] \\ But OC = r \cos θ \\ or B_{AB} = \frac{μ_{0} I}{2 πr} \tan θ \end{array}$
Magnetic field due to circular portion,
$B_{AB}' = \frac{μ_{0} I}{2 r} (\frac{2 π - 2 θi}{2 π}) = \frac{μ_{0} I}{2 πr} (π - θ)$
Total magnetic field
$\begin{array}{l} = \frac{μ_{0} I}{2 πr} \tan θ + \frac{μ_{0} I}{2 πr} (π - θ) \\ = \frac{μ_{0} I}{2 πr} [\tan θ + π - θ] \end{array}$

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