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^-7T ∙ 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 carrying current I is given by:$$B = \frac{\mu_0 I}{2\pi r}$$where r is the distance from the wire. In this problem, the wire is a tube with radius R = 3.0 mm = 3.0 × 10^-3 m, and the magnetic field just outside the tube is B = 44.0 × 10^-4 T. Therefore, the current flowing through the tube is:$$I = \frac{2\pi rB}{\mu_0} = \frac{2\pi (3.0 imes 10^{-3} ext{ m})(44.0 imes 10^{-4} ext{ T})}{4\pi imes 10^{-7} ext{ T} \cdot ext{m/A}} = 66 ext{ A}$$

A Tube with a 3