First slide

Magnetic field due to a current carrying circular ring

Question

An infinite, straight wire has two concentric loops of radii a and b carrying equal currents in opposite directions as shown. The magnetic field at the common centre is zero for

Moderate

A

$\frac{a}{b} = \frac{π - 1}{π}$
B

$\frac{a}{b} = \frac{π}{π + 1}$
C

$\frac{a}{b} = \frac{π - 1}{π + 1}$
D

$\frac{a}{b} = \frac{π + 1}{π - 1}$

Solution

$\begin{array}{l} B_{centre} = 0 \\ \frac{μ_{0} I}{4 πb} ⊙ + \frac{μ_{0} I}{4 πb} ⊙ + \frac{μ_{0} I}{2 b} ⊙ + \frac{μ_{0} I}{2 a} \otimes = 0 \\ \frac{μ_{0} I}{2 πb} + \frac{μ_{0} I}{2 b} - \frac{μ_{0} I}{2 a} = 0 \\ \frac{1}{2 πb} + \frac{1}{2 b} = \frac{1}{2 a} \\ \frac{a}{b} = \frac{π}{π + 1} \end{array}$

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