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 current I?

Options:

μ₀I/(4R)
μ₀I/(2R)
μ₀I/(πR)
μ₀I/(8R)

Correct Answer: μ₀I/(πR)

Solution:

The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R) for the semicircle, which is half of the full circular loop.

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

Practice Questions

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

μ₀I/(4R)
μ₀I/(2R)
μ₀I/(πR)
μ₀I/(8R)

Questions & Step-by-Step Solutions

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

Step 1: Understand that we have a wire shaped like a semicircle.
Step 2: Recognize that the wire carries a current, denoted as I.
Step 3: Identify the center of the semicircle where we want to find the magnetic field.
Step 4: Recall the formula for the magnetic field at the center of a full circular loop, which is B = μ₀I/(2R), where R is the radius of the circle.
Step 5: Since we only have a semicircle, the magnetic field at the center will be half of that of a full circle.
Step 6: Therefore, the magnetic field at the center of the semicircle is B = (1/2) * (μ₀I/(2R)) = μ₀I/(4R).
Step 7: Conclude that the magnetic field at the center of the semicircle is B = μ₀I/(4R).

Magnetic Field Due to Current – 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 Current-Carrying Wires – Recognizing the relationship between the shape of the wire and the resulting magnetic field at specific points.

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

What’s inside this PDF?

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

Practice Questions

Questions & Step-by-Step Solutions

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