A circular loop of radius R carries a current I. What is the magnetic field at t

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Question: A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop according to the Biot-Savart Law?

Options:

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).

A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop according to the Biot-Savart Law?

A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop according to the Biot-Savart Law?

Step 1: Understand that a circular loop carries a current I.
Step 2: Recall the Biot-Savart Law, which helps us calculate the magnetic field due to a current-carrying conductor.
Step 3: Identify that we want to find the magnetic field at the center of the circular loop.
Step 4: Recognize that the formula for the magnetic field B at the center of a circular loop is derived from the Biot-Savart Law.
Step 5: Use the formula B = (μ₀I)/(2R), where μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.
Step 6: Conclude that the magnetic field at the center of the loop is B = (μ₀I)/(2R).

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.