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)
Struggling with Physics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple 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)
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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