# Magnetic path length for partially wound toroidal transformer core

According to Wikipedia, magnetic path length is defined as "the effective length of a closed magnetic loop inside a magnetic core made of ferromagnetic material." Thus, for a toroidal core that is wound all the way around, the magnetic path length would be $2\pi r$. I'm curious if this definition holds even if the core is only partially wound.

For example, if I wind a coil to drive the core 1/4 of the way around and wind another coil to measure the magnetic flux density on a non-overlapping part of the core also 1/4 of the way around, is the magnetic path length the same as the above or would I divide by 4?

Your making a transformer, the ratio windings $\frac{N_p}{N_s}$ determine the voltage (and the current) from coil to coil. The magnetic path length is the same for both coils. Since most of the magnetic field is contained in the core (there is some leakage) where you put the coils on the core is not relevant in the general sense, only the number of coils relative to one another. This assumes the core is continous,
$$\frac{V_p}{V_s}= \frac{I_s}{I_p}= \frac{N_p}{N_s}$$ Source: https://en.wikipedia.org/wiki/Transformer