found http://webphysics.davidson.edu/physlet_resources/bu_semester2/c18_generators.html

the explanation is good.
A electric motor is a device for transforming electrical energy into mechanical energy; an electric generator does the reverse, using mechanical energy to generate electricity. At the heart of both motors and generators is a wire coil in a magnetic field. In fact, the same device can be used as a motor or a generator.

When the device is used as a motor, a current is passed through the coil. The interaction of the magnetic field with the current causes the coil to spin. To use the device as a generator, the coil is spun, inducing a current in the coil.

Let's say we spin a coil of N turns and area A at a constant rate in a uniform magnetic field B. By Faraday's law, the induced emf is given by:

? = -N d(BA cos(?))/dt

B and A are constants, and if the angular speed w of the loop is constant the angle is:
? = wt

The induced emf is then:

? = -NBA d(cos(wt))/dt = wNBA sin(wt) = ?o sin(wt)

Spinning a loop in a magnetic field at a constant rate is an easy way to generate sinusoidally oscillating voltage...in other words, to generate AC electricity. The amplitude of the voltage is:
?o = wNBA

In North America, AC electricity from a wall socket has a frequency of 60 Hz. but in Singapore is 50 Hz The angular frequency of coils or magnets where the electricity is generated is therefore 60 Hz in USA or 50 Hz in Singapore.

To generate DC electricity, use the same kind of split-ring commutator used in a DC motor to ensure the polarity of the voltage is always the same. In a very simple DC generator with a single rotating loop, the voltage level would constantly fluctuate. The voltage from many loops (out of synch with each other) is usually added together to obtain a relatively steady voltage.

Rather than using a spinning coil in a constant magnetic field, another way to utilize electromagnetic induction is to keep the coil stationary and to spin permanent magnets (providing the magnetic field and flux) around the coil. A good example of this is the way power is generated, such as at a hydro-electric power plant. The energy of falling water is used to spin permanent magnets around a fixed loop, producing AC power.