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 according to Ampere\'s Law?

Options:

Correct Answer: μ₀I/2R

Solution:

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

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?

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?

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.

Ampere's Law – Ampere's Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
Magnetic Field of a Current Loop – The magnetic field at the center of a circular current-carrying loop can be derived from Ampere's Law and is dependent on the current and radius of the loop.