# Alternatic Current Derivation

## Main Question or Discussion Point

Hello all,
I'm trying to find the derivation for the alternating signal. For example,

let b=width of loop
a=length of loop
Hence,
$$ε=vLB=vaB=ωraB=\frac{1}{2}ωabB=\frac{1}{2}ωAB$$
I cannot seem to find the derivation of how one gets from this step, to the sinusoidal waveform. Any help is greatly appreciated.

Related Electrical Engineering News on Phys.org
256bits
Gold Member
Your sin comes from the fact that in the up and down direction V has a magnitude that varies sinusoudally. ie At the top and bottom, 0 deg and 180 deg, if y is the vertical direction , Vy=0. At 90 deg and 270 deg Vy has its maximum value wr.

So, essentially the first part of the derivation has nothing to do with the rest? My notes jump from the first part that I depicted directly to the sinusoid function, without any intermediate steps.