If a wire is bent into a semicircular shape, what is the magnetic field at the c

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Question: If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to the current I?

Options:

Correct Answer: μ₀I/(4R)

Solution:

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

If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to the current I?

If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to the current I?

Step 1: Understand that a semicircular wire is half of a full circle.
Step 2: Know that when current I flows through the wire, it creates a magnetic field around it.
Step 3: Recognize that the center of the semicircle is the point where we want to find the magnetic field.
Step 4: Use the formula for the magnetic field due to a current-carrying wire: B = μ₀I/(4R), where μ₀ is the permeability of free space and R is the radius of the semicircle.
Step 5: Identify that R is the radius of the semicircle, which is the distance from the center to the wire.
Step 6: Substitute the values of I and R into the formula to calculate the magnetic field B at the center.

Magnetic Field due to Current-Carrying Wire – Understanding how current flowing through a wire generates a magnetic field, particularly in curved shapes like semicircles.
Biot-Savart Law – Application of the Biot-Savart Law to calculate the magnetic field produced by a segment of current-carrying wire.
Geometry of the Problem – Recognizing the significance of the radius (R) of the semicircle in determining the magnetic field strength.