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What is the magnetic moment of a circular loop of radius r carrying a current I?

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Question: What is the magnetic moment of a circular loop of radius r carrying a current I? (2021)

Options:

  1. πr²I
  2. 2πrI
  3. Ir²
  4. πrI

Correct Answer: πr²I

Exam Year: 2021

Solution: 

The magnetic moment (μ) of a circular loop is given by μ = I × A, where A is the area of the loop. For a circular loop, A = πr², thus μ = I × πr² = πr²I.

What is the magnetic moment of a circular loop of radius r carrying a current I?

Practice Questions

Q1
What is the magnetic moment of a circular loop of radius r carrying a current I? (2021)
  1. πr²I
  2. 2πrI
  3. Ir²
  4. πrI

Questions & Step-by-Step Solutions

What is the magnetic moment of a circular loop of radius r carrying a current I? (2021)
  • Step 1: Understand that the magnetic moment (μ) is a measure of the strength of a magnetic source.
  • Step 2: Know that for a circular loop carrying a current, the magnetic moment is calculated using the formula μ = I × A.
  • Step 3: Identify that A is the area of the circular loop.
  • Step 4: Calculate the area (A) of the circular loop using the formula A = πr², where r is the radius of the loop.
  • Step 5: Substitute the area (A) back into the magnetic moment formula: μ = I × πr².
  • Step 6: Simplify the expression to get the final formula for the magnetic moment: μ = πr²I.
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