Magnetic Field Produced by Loops and Solenoids Video Lessons

Concept

Problem: A loop of wire is in the shape of two concentric semicircles as shown. (Figure 1) The inner circle has radius a; the outer circle has radius b. A current I flows clockwise through the outer wire and counterclockwise through the inner wire. What is the magnitude of the magnetic field at the center of the semicircles?

FREE Expert Solution

The magnetic field at the center of the semicircle due to inner wire of radius a is expressed as:

${\mathbit{B}}_{\mathbf{a}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{a}}$

Similarly, the magnetic field at the center of the semicircle due to the outer wire of radius b is:

${\mathbit{B}}_{\mathbf{b}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{b}}$

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Problem Details

A loop of wire is in the shape of two concentric semicircles as shown. (Figure 1) The inner circle has radius a; the outer circle has radius b. A current I flows clockwise through the outer wire and counterclockwise through the inner wire. What is the magnitude of the magnetic field at the center of the semicircles?