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Using Biot-Savart Law, what is the magnetic field at the center of a circular lo

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

Options:

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

Correct Answer: μ₀I/(2πR)

Solution: 

The magnetic field at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2R) and for a complete loop, it simplifies to B = μ₀I/(2πR).

Using Biot-Savart Law, what is the magnetic field at the center of a circular lo

Practice Questions

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

Questions & Step-by-Step Solutions

Using Biot-Savart Law, what is the magnetic field at the center of a circular loop of radius R carrying current I?
  • Step 1: Understand the Biot-Savart Law, which states that the magnetic field (B) created by a small segment of current-carrying wire is proportional to the current (I) and inversely proportional to the distance (r) from the wire segment to the point where the field is measured.
  • Step 2: For a circular loop, every small segment of the loop contributes to the magnetic field at the center of the loop.
  • Step 3: The distance from any point on the loop to the center is constant and equal to the radius (R) of the loop.
  • Step 4: The total magnetic field at the center is the sum of the contributions from all the small segments of the loop.
  • Step 5: Using the Biot-Savart Law, we can derive that the magnetic field at the center of the loop is B = (μ₀I)/(2R) for a single loop.
  • Step 6: If the loop is complete and we consider the full circular path, we can simplify this to B = (μ₀I)/(2πR).
  • Biot-Savart Law – The Biot-Savart Law describes how electric currents produce magnetic fields, particularly in the context of circular loops.
  • Magnetic Field Calculation – The question tests the ability to apply the Biot-Savart Law to calculate the magnetic field at a specific point (the center of a loop).
  • Circular Loop Geometry – Understanding the geometry of a circular loop and how it affects the magnetic field distribution.
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