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AIIMS 2012
Exam
AIIMS
Year
2012
Subject
Physics
Chapter
Magnetic Effects of Current

AIIMS 2012 · Physics · Magnetic Effects of Current

Assertion : A planar circular loop of area A and carrying current I...

Assertion : A planar circular loop of area AA and carrying current II is equivalent to magnetic dipole of dipole moment M=IAM=I A.Reason : At large distances, magnetic field of circular loop and magnetic dipole is same.

Options

  1. AIf both assertion and reason are true and reason is the correct explanation of assertion.
  2. BIf both assertion and reason are true but reason is not the correct explanation of assertion.
  3. CIf assertion is true but reason is false.
  4. DIf both assertion and reason are false.

Correct answer

A. If both assertion and reason are true and reason is the correct explanation of assertion.

Step-by-step solution

Magnetic field due to a circular loop carrying current I is given as B=μ04π2πIr2(r2+x2)3/2B=\frac{\mu_0}{4 \pi} \frac{2 \pi I r^2}{\left(r^2+x^2\right)^{3 / 2}} where, r=r= radius of loop x=x= distance from centre of loop For large distances, (x>>r)(x>>r), ∴B=μ04π2IAx3=μ04π2Mx3\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=IA=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.
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