Open Question
Find an expression for the magnetic field strength at the center (point P) of the circular arc in FIGURE P29.45.
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29. Sources of Magnetic Field
Biot-Savart Law (Calculus)
Multiple Choice
What is the magnetic field at the center of the following ring of current?
A
μ0i/(2r)
B
μ0i/(πr2)
C
μ0i/(2πr)
D
μ0i / √(2πr)
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Verified step by step guidance1
Identify the problem: We need to find the magnetic field at the center of a circular loop carrying a current i. The radius of the loop is r.
Recall the formula for the magnetic field at the center of a circular loop: The magnetic field B at the center of a loop of radius r carrying a current i is given by B = (μ₀i)/(2r), where μ₀ is the permeability of free space.
Understand the direction of the magnetic field: According to the right-hand rule, if the current flows in a counterclockwise direction, the magnetic field at the center points out of the plane of the loop.
Compare with the given options: The correct formula for the magnetic field at the center of the loop is μ₀i/(2r), which matches one of the provided options.
Conclude the solution: Based on the formula and the options given, the correct answer is μ₀i/(2r).
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