| ASSERTION: A planar circular loop of area A and Carrying Current I is equivalent to magnetic dipole of dipole moment M = IA. |
| REASON: At large distances, magnetic field of circular loop and magnetic dipole is same. |
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true and reason is not the correct explanation of assertion.
C) If assertion is true but reason is false.
D) If both assertion and reason are false.
E) If assertion is false but reason is true.
Correct Answer: A
Solution :
Magnetic field due to a circular loop carrying current I is given as \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi I{{r}^{2}}}{{{\left( {{r}^{2}}+{{x}^{2}} \right)}^{\frac{3}{2}}}}\] Where, r = radius of loop x = distance from center of loop For large distance, (x > > r), \[\therefore \,\,\,B=\frac{{{\mu }_{0}}}{4\pi }\frac{2IA}{{{x}^{3}}}=\frac{{{\mu }_{0}}}{4\pi }\frac{2M}{{{x}^{3}}}\] Where M = IA = magnetic 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.
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