First slide

Magnetic dipole - Moving charges and magnetism

Question

A conductor carries a constant current I along the closed path abcdefgha involving 8 of the 12 edges of length l . Find the magnetic dipole moment of the closed path.

Moderate

A

$l^{2} I \hat{j}$
B

$l^{2} I \hat{k}$
C

$l^{2} I^{2} \hat{j}$
D

$l^{2} I (- \hat{j})$

Solution

Closed path is a superposition of the loops bcfgb, abgha, and cdefc.
$∴$ The magnetic moments of the three loops are

$loop -1 (b c f g b) {\bar{m}}_{1} = i l^{2} \hat{j} loop -2 (a b g h a) {\bar{m}}_{2} = - l^{2} i \hat{i} loop - 3 (c d e f c) {\bar{m}}_{3} = + l^{2} i \hat{i} ∴ {\bar{M}}_{n e t} = {\bar{M}}_{1} + {\bar{M}}_{2} + {\bar{M}}_{3} = i l^{2} \hat{j} - l^{2} i \hat{i} + l^{2} i \hat{i} = i l^{2} \hat{j}$

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