If a circular loop of radius R carries a current I, what is the magnetic field a

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Question: If a circular loop of radius R carries a current I, what is the magnetic field at the center of the loop?

Options:

Correct Answer: μ₀I/2R

Solution:

Using Ampere\'s Law, B = μ₀I/2R at the center of a circular loop.

If a circular loop of radius R carries a current I, what is the magnetic field at the center of the loop?

If 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 wire shaped in a circle.
Step 2: Know that when current (I) flows through the wire, it creates a magnetic field.
Step 3: Identify the radius of the loop, which is given as R.
Step 4: Recall Ampere's Law, which helps us find the magnetic field (B) created by the current.
Step 5: Use the formula for the magnetic field at the center of a circular loop: B = (μ₀ * I) / (2 * R).
Step 6: Here, μ₀ is a constant called the permeability of free space.
Step 7: Plug in the values of I and R into the formula to find the magnetic field at the center.

Magnetic Field of a Current Loop – The magnetic field at the center of a circular loop carrying current can be derived using Ampere's Law or Biot-Savart Law.
Ampere's Law – A fundamental law relating the integrated magnetic field around a closed loop to the electric current passing through the loop.