The magnitude of the induced voltage depends on two factors: (1) the number of turns of a coil, and (2) how fast the conductor cuts across the magnetic lines of force, or flux. Equation (1-20) is the mathematical representation for Faraday's Law of Induced Voltage.

where

V_ind = induced voltage, V

Example 1: Given: Flux = 4 Wb. The flux increases uniformly to 8 Wb in a period of 2 seconds. Find induced voltage in a coil that has 12 turns, if the coil is stationary in the magnetic field.

Solution:

then

Example 2: In Example 1, what is the induced voltage, if the flux remains 4 Wb after 2 s?

Solution:

No voltage is induced in Example 2. This confirms the principle that relative motion must exist between the conductor and the flux in order to induce a voltage.

Lenz's Law

Lenz's Law determines the polarity of the induced voltage. Induced voltage has a polarity that will oppose the change causing the induction. When current flows due to the induced voltage, a magnetic field is set up around that conductor so that the conductor's magnetic field reacts with the external magnetic field. This produces the induced voltage to oppose the change in the external magnetic field. The negative sign in equation (1-20) is an indication that the emf is in such a direction as to produce a current whose flux, if added to the original flux, would reduce the magnitude of the emf.

Summary

The important information contained in this chapter is summarized below.

Magnetic Circuits Summary

Simple magnetic circuit magnetic flux () is proportional to the magnetomotive force (F_m) and indirectly proportional to the reluctance (R) in a circuit.

A BH magnetization curve shows how much magnetic flux density (B) results from increasing magnetic flux intensity. The "knee" identifies the point where increasing flux intensity (H) results in a minimal increase in flux density (B).

Hysteresis losses are caused by reversing current direction thousands of times in a coil.

Faraday's Law of Induced Voltage depends on the number of turns of a coil and how fast the conductor cuts across the magnetic lines of force or flux.

Lenz's Law states that an induced voltage will have a polarity that will oppose the magnetic field that caused the induced voltage.