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

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

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).

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