Q111 / 180 · AIIMS 2012 · Physics
Assertion : A planar circular loop of area $A$ and carrying current $I$ is equivalent to magnetic dipole of dipole moment $M=I A$.Reason : At large distances, magnetic field of circular loop and magnetic dipole is same.
- Correct answerAIf both assertion and reason are true and reason is the correct explanation of assertion.
- BIf both assertion and reason are true but reason is not the correct explanation of assertion.
- CIf assertion is true but reason is false.
- DIf both assertion and reason are false.
Solution
Magnetic field due to a circular loop
carrying current I is given as
$B=\frac{\mu_0}{4 \pi} \frac{2 \pi I r^2}{\left(r^2+x^2\right)^{3 / 2}}$
where, $r=$ radius of loop $x=$ distance from centre of loop For large distances, $(x>>r)$,
$\therefore \quad B=\frac{\mu_0}{4 \pi} \frac{2 I A}{x^3}=\frac{\mu_0}{4 \pi} \frac{2 M}{x^3}$
where $M=I A=$ magnetic dipole moment of current loop which is equal to the magnetic field due to magnetic dipole.
Thus, the current loop can be considered as a magnetic dipole.
Hence, the correct answer is option: 'A'.