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In a circular loop of radius R carrying a current I, what is the magnetic field

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Question: In a circular loop of radius R carrying a current I, what is the magnetic field at the center of the loop according to the Biot-Savart Law?

Options:

  1. B = (μ₀I)/(2R)
  2. B = (μ₀I)/(4R)
  3. B = (μ₀I)/(R)
  4. B = (μ₀I)/(πR)

Correct Answer: B = (μ₀I)/(2R)

Solution: 

The magnetic field at the center of a circular loop of radius R carrying current I is given by B = (μ₀I)/(2R).

In a circular loop of radius R carrying a current I, what is the magnetic field

Practice Questions

Q1
In a circular loop of radius R carrying a current I, what is the magnetic field at the center of the loop according to the Biot-Savart Law?
  1. B = (μ₀I)/(2R)
  2. B = (μ₀I)/(4R)
  3. B = (μ₀I)/(R)
  4. B = (μ₀I)/(πR)

Questions & Step-by-Step Solutions

In a circular loop of radius R carrying a current I, what is the magnetic field at the center of the loop according to the Biot-Savart Law?
Correct Answer: B = (μ₀I)/(2R)
  • Step 1: Understand that we have a circular loop with a radius R.
  • Step 2: Know that the loop carries an electric current I.
  • Step 3: Recall the Biot-Savart Law, which helps us calculate the magnetic field created by a current-carrying wire.
  • Step 4: Recognize that at the center of the circular loop, the magnetic field can be calculated using a specific formula.
  • Step 5: The formula for the magnetic field B at the center of the loop is B = (μ₀I)/(2R), where μ₀ is the permeability of free space.
  • Step 6: Substitute the values of I and R into the formula to find the magnetic field at the center.
  • Biot-Savart Law – The Biot-Savart Law describes how electric currents produce magnetic fields, particularly in the context of circular loops.
  • Magnetic Field Calculation – Understanding how to calculate the magnetic field at a specific point due to a current-carrying conductor.
  • Circular Loop Geometry – Recognizing the significance of the radius of the loop in determining the strength of the magnetic field.
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