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A conductor carries a constant current I...

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.

Text Solution

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The closed path is a superposition of three loops: bcfgb, abgha and cdefc.

The magnetic moments of the three loops are :
Loop 1(bcfgb): `vecmu_1=l^2Ihatj`
2(abgha): `vecmu_2=-l^2Ihati`
3(cdefc): `vecmu_3=l^2Ihati`
The total magnetic moment is `vecmu=vecmu_1+vecmu_2+vecmu_3 or vecmu=l^2Ihatj`.
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