# Toroidal Solenoid

If I have a solenoid in the shape of a toroid (i.e. solenoid joined end to end) the magnetic field produced by the flow of charge will produce a concentrated magnetic field within the coil.

How would I go about calculating the size of the magnetic field outside of the coil due to magnetic field leakage?

Any advice much appreciated.

LB

## Answers and Replies

stevendaryl
Staff Emeritus
If I have a solenoid in the shape of a toroid (i.e. solenoid joined end to end) the magnetic field produced by the flow of charge will produce a concentrated magnetic field within the coil.

How would I go about calculating the size of the magnetic field outside of the coil due to magnetic field leakage?

Any advice much appreciated.

LB

I think that a good approximation would be to assume that the magnetic field $\vec{B}$ inside the soldenoid is directed perpendicular to the plane of each coil and is zero outside of the solenoid. Then you can use Ampere's law to compute it:

$\int B \cdot d\mathcal{l} = \mu I$

The meaning of that equation is that if you imagine drawing a closed loop that encloses a bunch of wires, then the total current enclosed by the loop is equal to the line integral of $B$ around the loop.