Answer to Question #174799 in Electricity and Magnetism for Pushpo

Question

Find an expression which shows the conversion of mechanical energy in to electrical energy through magnetic induction.

Answer 1

Mechanical energy to electrical energy conversion is done via a generator.

Therefore the expression from the principle of conservation of energy is as shown below

$W_e=W_m+W_f+W_{loss}$

W_e is the electrical energy

W_m is the mechanical energy

W_f is the field stored energy

W_loss is the lost energy during the conversion. (In electrical, I²R, mechanical is friction, magnetic eddy currents

Core loss, also known as Iron Loss, is ultimately caused by the alternating magnetic flux in the core. Furthermore, iron loss is split into hysteresis and eddy current losses.

It is a loss that happens in the core of a transformer when it is subjected to a change in alternating changes in magnetic flux subjected to the material. Which is responsible for the drop in the energy conversion rate degrading the performance and efficiency.

Due to unstable magnetic fields, failure happens which ultimately destroys the core without a stable magnetic field. Depending on the primary cause, they are being classified into two different losses

P_h=KƞB^1.6fV in Watts

Where ‘Kƞ‘ is constant depends on the material of the magnetic core.’

‘f‘ is the frequency in Hertz.

‘B‘ is the highest flux density.

‘V‘ is Material Volume.

Due to alternating amounts of magnetic flux, an electromotive force is induced into the core of the transformer.

Here is the formula for calculation

P_e=K_eB²f²t²V in Watts

where ‘K_e‘ is coefficient constant.

‘f ‘is the frequency in Hertz.

‘B‘ is the highest flux density in weber per meter square.

‘T‘ is lamination material thickness in meters.

‘V‘ is the material volume in cubic meters.

$dW_e=dW_m+dW_f+W_{loss}$ we can neglect the losses

$W_m= \tau \omega$

$e=N \frac{d \mu}{dt}= \frac{d \lambda}{dt}$

$d \omega _e=ie dt=i \frac{d \lambda}{dt}.dt=id\lambda$

$W_f=\int_0^\lambda id\lambda$

$W_e=\tau \omega +\int_0^\lambda id\lambda-(I^2R+KƞB^{1.6}fV +K_eB^2f^2t^2V)$