hi guys ,

need help with understanding the mathematics of the electrical generator theory.

analyse the operational aspects of the wire loop and their effects on the shape of the generated voltage at the terminals of the loop. Take an operating point where the wire loop is expected to generate 2 V., and running at speed of 500 rpm

information that i know,

need help on understanding and generating a mathematical equation. i presume its all to do with Faraday law, but dont know how everything connects. would be grateful if someone can explain it for me

 

The EMF generated in the conductor loop is proportional to the rate of change of magnetic field strength in the enclosed area, which of course varies with the projected area as the loop rotates. Time to practice your calculus chops.

 

The EMF generated in the conductor loop is proportional to the rate of change of magnetic field strength in the enclosed area, which of course varies with the projected area as the loop rotates. Time to practice your calculus chops.

Hey thanks,
why do i need to practice calculus?
so i am supposed to generate a mathematical equation then model that on Simulink and analyse the operation. im kind of stuck on the part of how to make this mathematical equation :|

 

why do i need to practice calculus?

The voltage generated is proportion to the projected loop area in the magnetic field as it varies with time.
So you need to write an equation relating the rotational loop area with respect to time as the independent variable.
If you can do that without calculus, fine, but you need some sort of mathematics to write that equation.

What is your mathematical knowledge?

 

so basically, the voltage produced is equal to the effective area of the loop which is perpendicular to the magnetic field at different angles with respect to time. the actual area of the loop is not changing just the anglle is .

would this be a fair mathematical representation
EMF generated = BA (Δcosθ/Δt)

where B is the magnetic field, A is effective area , cosθ is the angle perpendicular to the magnetic field over time?

 

so basically, the voltage produced is equal to the effective area of the loop which is perpendicular to the magnetic field at different angles with respect to time. the actual area of the loop is not changing just the anglle is .

would this be a fair mathematical representation
EMF generated = BA (Δcosθ/Δt)

where B is the magnetic field, A is effective area , cosθ is the angle perpendicular to the magnetic field over time?

which will be simplified to

=BA (dcosθ/dt)
=BA -sinθ (dθ/dt) ∴ω=dθ/dt
= BA -sinθ (ω)

 

Close. There's a pretty good coverage of it here:
http://www.physics.ohio-state.edu/~humanic/p112_lecture13.pdf