Toroidal Coil in Measuring Alternating Current at a Distance

Abstract

This article discusses the use of a toroidal coil in measuring alternating current from a straight current-carrying wire passing perpendicularly through the coil. The sinusoidally oscillating current generates a sinusoidally oscillating magnetic field in its vicinity. This, in turn, induces a sinusoidally oscillating emf in the toroid. This (measured) emf can be used in order to calculate the magnitude of the electric current in the wire. The use of such technique might be sensitive to the location of the point at which the wire passes through the toroid. If the location is not known very precisely, this might cause errors in the value of the calculated current. We wanted to study if the result does not depend on the location of the wire at all, as is usually stated, or not. The study was done by deriving a single analytical formula for finding out the calculated current with the wire passing through any given point inside the toroid. This formula was then solved at more than 2300 points inside a toroid to see if the location of the wire affects the result or not.