A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be 44.0 × 10^-4 T. If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and do not screen magnetism, what is the magnitude of the current flowing through the tube? (μ₀ = 4π × 10^-7 T ∙ m/A) A) 66 A B) 132 A C) 829 A D) 415 A

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Quizplus · Accepted Answer

The magnetic field outside a long, straight wire is given by:$$B = \frac{\mu_0 I}{2\pi r}$$where:* B is the magnetic field (in teslas)* μ0 is the permeability of free space (4π × 10^-7 T ∙ m/A)* I is the current (in amperes)* r is the distance from the wire (in meters)In this problem, we are given:* B = 44.0 × 10^-4 T* r = 3.0 mm = 3.0 × 10^-3 mWe can solve for I by rearranging the equation:$$I = \frac{2\pi rB}{\mu_0}$$$$I = \frac{2\pi (3.0 	imes 10^{-3} 	ext{ m})(44.0 	imes 10^{-4} 	ext{ T})}{4\pi 	imes 10^{-7} 	ext{ T} \cdot 	ext{m/A}}$$$$I = 66 	ext{ A}$$Therefore, the magnitude of the current flowing through the tube is 66 A.

A Tube with a 3