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A circular loop of radius R carries a current I. What is the magnetic field at t

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Question: A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop?

Options:

  1. μ₀I/(2R)
  2. μ₀I/R
  3. μ₀I/(4R)
  4. μ₀I/(8R)

Correct Answer: μ₀I/R

Solution: 

The magnetic field at the center of a circular loop carrying current I is given by the formula B = (μ₀I)/(2R), where μ₀ is the permeability of free space.

A circular loop of radius R carries a current I. What is the magnetic field at t

Practice Questions

Q1
A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop?
  1. μ₀I/(2R)
  2. μ₀I/R
  3. μ₀I/(4R)
  4. μ₀I/(8R)

Questions & Step-by-Step Solutions

A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop?
  • Step 1: Understand that a circular loop is a shape that is round and has a radius R.
  • Step 2: Know that the loop carries an electric current I, which means that electric charge is flowing through it.
  • Step 3: Recognize that the magnetic field is a force field created by the electric current in the loop.
  • Step 4: Learn the formula for the magnetic field at the center of the loop, which is B = (μ₀I)/(2R).
  • Step 5: Identify that μ₀ is a constant called the permeability of free space, which helps in calculating the magnetic field.
  • Step 6: Substitute the values of I (current) and R (radius) into the formula to find the magnetic field B.
  • Magnetic Field Due to Current – Understanding how a current-carrying loop generates a magnetic field and the application of the relevant formula.
  • Permeability of Free Space – Knowledge of the constant μ₀ and its role in calculating magnetic fields in free space.
  • Geometry of Circular Loops – Recognizing the significance of the radius R in determining the strength of the magnetic field at the center of the loop.
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