What is meant by excitation?

"Self Excited vs Magneto". Licensed under PD-US via Wikipedia

Electric generators work on the principle of electromagnetic induction. The essential part of this principle is the magnetic field. The magnetic field is produced from a d.c. power source from an exciter that is part of the generator system. The main requirement for electricity generation as per the basic principle is a magnetic field. The generator while producing electricity also has to produce the excitation current at a constant voltage for the electrical system to work properly. Controlling the magnetic field controls the voltage output of the generator.

The rotor or field coils in a generator produce the magnetic flux that is essential to the production of the electric power. The rotor is rotating electromagnet that requires a d.c. electric power source to excite the magnetic field. This power comes from an exciter.

Exciter is a device that provides a magnetizing current for the electromagnets in a motor or generator. There are two types of exciter, static exciter and rotory exciter. Rotory exciter is an additional small generator mounted on shaft of main generator. It will supply d.c. voltage to the rotory poles through slip ring and brushes. If it is an a.c. exciter, output of a.c. exciter is rectified by rotating diodes and supply d.c. to main field poles.

Divergence Theorem

It gives the facility to convert surface integral into its equivalent volume integral.

Representational Image
Photo Credit - www.wikipedia.com

Statement:- It states that the surface integral of a normal component of any vector function on a closed surface is equal to the volume integral of the divergence of vector function.
Proof:-  The total charge enclosed by volume △V is given by

........(1)

The total outward flux coming out from the volume is △V equal to the charge enclosed.

△Ψ = △Q = charge density x volume

△Ψ = △Q =ρ_v△V = ρ_v△x△y△z.......(2)

From equation (1) and (2)

........(3)

The divergence of D is given by 

........(4)

From (3) and (4) 

According to Gauss's Law

ψ = Q