A hollow cylinder with an inner radius of 4.0 mm and an outer radius of 30 mm conducts a 3.0-A current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point 12 mm from its center? (μ₀ = 4π × 10^-7 T ∙ m/A) A) 7.2 × 10^-6 T B) 8.0 × 10^-6 T C) 8.9 × 10^-7 T D) 7.1 × 10^-8 T

Question

Quizplus · Accepted Answer

The magnetic field at a point 12 mm from the center of a hollow cylinder with an inner radius of 4.0 mm and an outer radius of 30 mm carrying a current of 3.0 A is given by:$$B = \frac{\mu_0 I}{2\pi r}$$where:* B is the magnetic field in teslas (T)* μ0 is the permeability of free space (4π × 10^-7 T ∙ m/A)* I is the current in amperes (A)* r is the distance from the center of the cylinder to the point where the magnetic field is being measured in meters (m)Plugging in the given values, we get:$$B = \frac{(4π × 10^-7 T ∙ m/A)(3.0 A)}{2π(0.012 m)} = 7.2 × 10^-6 T$$Therefore, the magnitude of the magnetic field at a point 12 mm from the center of the hollow cylinder is 7.2 × 10^-6 T.

A Hollow Cylinder with an Inner Radius of 4