If a wire carrying current I is bent into a semicircular arc of radius R, what i

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Question: If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?

Options:

Correct Answer: μ₀I/(4R)

Solution:

The magnetic field at the center of a semicircular arc of radius R carrying current I is given by B = μ₀I/(4R).

If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?

If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?

Step 1: Understand that a wire carrying current creates a magnetic field around it.
Step 2: Recognize that when the wire is bent into a semicircular shape, we need to find the magnetic field at the center of that semicircle.
Step 3: Recall the formula for the magnetic field due to a straight wire segment, which is related to the current and the distance from the wire.
Step 4: For a semicircular arc, the magnetic field at the center can be derived from the formula for a full circular loop, but since we only have half, we adjust the formula.
Step 5: The formula for the magnetic field at the center of a semicircular arc is B = μ₀I/(4R), where μ₀ is the permeability of free space, I is the current, and R is the radius of the arc.
Step 6: Conclude that this formula gives us the magnetic field strength at the center of the semicircular arc.

Magnetic Field due to Current-Carrying Wire – Understanding how to calculate the magnetic field produced by a current-carrying wire, particularly in curved shapes like a semicircular arc.
Biot-Savart Law – Application of the Biot-Savart Law to determine the magnetic field at a point due to a segment of current-carrying wire.
Geometry of Magnetic Fields – Recognizing the geometric implications of the wire's shape on the resulting magnetic field.