As shown in the figure, a wire is bent into the shape of a tightly closed omega (Ω), with a circular loop of radius 4.0 cm and two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the x-axis. The wire carries a 5.0-A current, as shown. What is the magnitude of the magnetic field at the center of the loop? (μ₀ = 4π × 10^-7 T ∙ m/A) A) 25 µT B) 40 µT C) 54 µT D) 80 µT E) 104 µT

Question

Quizplus · Accepted Answer

We can use the formula for the magnetic field at the center of a circular loop:

B = μ₀I/2r

where μ₀ is the permeability of free space, I is the current, and r is the radius of the loop.

In this case, μ₀I = (4π × 10^-7 T ∙ m/A)(5.0 A) = 2.0 × 10^-6 T ∙ m

and r = 4.0 cm = 0.04 m

Substituting these values gives:

B = (2.0 × 10^-6 T ∙ m)/(2(0.04 m)) = 5.0 × 10^-5 T = 50 µT

Therefore, the best choice is C, 54 µT, which is the closest rounded value to our calculated result of 50 µT.

As Shown in the Figure, a Wire Is Bent into the Shape