Using Biot-Savart Law, what is the magnetic field at the center of a circular loop of radius R carrying current I?
Practice Questions
1 question
Q1
Using Biot-Savart Law, what is the magnetic field at the center of a circular loop of radius R carrying current I?
μ₀I/(2R)
μ₀I/(4R)
μ₀I/(πR)
μ₀I/(2πR)
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).
Questions & Step-by-step Solutions
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Q
Q: Using Biot-Savart Law, what is the magnetic field at the center of a circular loop of radius R carrying current I?
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).
Steps: 6
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).
