AP Physics C — Magnetic Field inside and outside a solenoid

A Solenoid is a tightly compacted coil of wire, much like a slinky. It has a number of turns , a length , and a radius .

When it carries a Current , a Magnetic Field is created inside the solenoid. The outside magnetic field is negligible.

As you get closer to the ends of a solenoid, the magnetic field breaks down. We typically only look at the magnetic field in the center of the solenoid. An “ideal” solenoid is infinitely long.

We can use Ampere’s Law to find the magnetic field inside the solenoid. Our Amperian Loop will be rectangular as seen below:

Then we do the math: