12.6 Solenoids and Toroids

What is the ratio of the magnetic field produced from using a finite formula over the infinite approximation for an angle $\theta$ of (a) $85 ° ?$ (b) $89 ° ?$ The solenoid has 1000 turns in 50 cm with a current of 1.0 A flowing through the coils

Explain why $\overset{\rightarrow}{B} = 0$ inside a long, hollow copper pipe that is carrying an electric current parallel to the axis. Is $\overset{\rightarrow}{B} = 0$ outside the pipe?

A solenoid is wound with 2000 turns per meter. When the current is 5.2 A, what is the magnetic field within the solenoid?

If a current is 2.0 A, how many turns per centimeter must be wound on a solenoid in order to produce a magnetic field of $2.0 \times 10^{−3} \text{T}$ within it?

Determine the magnetic field on the central axis at the opening of a semi-infinite solenoid. (That is, take the opening to be at $x = 0$ and the other end to be at
$x = \infty .$)

A solenoid with 25 turns per centimeter carries a current I. An electron moves within the solenoid in a circle that has a radius of 2.0 cm and is perpendicular to the axis of the solenoid. If the speed of the electron is $2.0 \times 10^{5} \text{m}/\text{s} ,$ what is I?

A toroid with a square cross section 3.0 cm $\times$ 3.0 cm has an inner radius of 25.0 cm. It is wound with 500 turns of wire, and it carries a current of 2.0 A. What is the strength of the magnetic field at the center of the square cross section?