# Magnetic Field in Solenoid question

## Homework Statement

Your physics lab demonstrator hands you a spool of copper wire and a battery (voltage V) and asks you to wind the wire around a hollow, cylindrical, cardboard tube (radius a) to make a solenoid of length 2L.

a) What is the amplitude of the magnetic field at the centre of the carboard tube (ie., on the axis, halfway between the ends) due to a single turn of wire at a distance z from the centre?

b) What is the amplitude of the magnetic field at the centre of the solenoid of length 2L?

c) How long should the solenoid be so that the magnetic field in PART B equals 60% of the value in an infinite solenoid?

d) In real life, for L much bigger than a, how does the magnetic field in PART B scale with L?

e) Suppose your physics lab class lasts for a very long time - long enough for you to wind a semi-infinite solenoid. What is the on-axis magnetic field at the end of the solenoid closest to you (i.e. not at infinity)?

f) What is the on-axis magnetic field a distance 2a beyond the end of the semi-infinite solenoid, as a fraction of your answer to PART E?

## Homework Equations

Biot-Savart Law, Ampere's Law (maybe some others?)

## The Attempt at a Solution

I can do a) using Biot-Savart Law, and b) using Ampere's Law. However I'm confused by the rest of the sections. Any help is welcome!