If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to current I?
Practice Questions
1 question
Q1
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)
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.
Questions & Step-by-step Solutions
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Q
Q: If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to current I?
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.
Steps: 7
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).
