If a circular loop of radius R carries a current I, what is the magnetic field at the center of the loop according to Ampere's Law?

1 question

1 item

Q: If a circular loop of radius R carries a current I, what is the magnetic field at the center of the loop according to Ampere's Law?

Solution: The magnetic field at the center of a circular loop is given by B = (μ₀I)/(2R).

Steps: 7

Step 1: Understand that a circular loop of wire carries an electric current I.
Step 2: Recognize that this current creates a magnetic field around the loop.
Step 3: Identify that we want to find the magnetic field specifically at the center of the loop.
Step 4: Recall Ampere's Law, which relates the magnetic field to the current and the geometry of the loop.
Step 5: Use the formula for the magnetic field at the center of a circular loop: B = (μ₀I)/(2R).
Step 6: In this formula, μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.
Step 7: Substitute the values of I and R into the formula to calculate the magnetic field B.