Need explanation on part of induction equation

[GarageTinker]

As part of a personal garage tinkering project, I am utilizing the equation (Faraday's?) to figure the voltage output of a DC induction coil (magnetic induction generator) with an air core and I have some questions about the equation: ∑ = -N{(∆B*A) / ∆t}.

Where "A" is the area of the coil, does the equation refer to the entire area of the coil or the entire area minus the area of the air core (which would leave just the area occupied by the coil wire)?

Also, am I correct in understanding that "∆t" refers to the length time for one full cycle from North to South and back to North?

I have been trying to teach myself the physics involved in this spare time project and I want to make sure I understand the math correctly. I would appreciate any assist or explanation that anyone could give. Thanks in advance.

 

[LeonhardEuler]

The "A" refers to the entire area of the coil. As for $\Delta t$, this refers to the time it takes for the magnetic flux to change by $\Delta B$. So if the field changes by 8 Tesla every 2 seconds then $\frac{\Delta B}{\Delta t}=4T/s$.

 

[GarageTinker]

Thank you for your help. Please clarify; if the difference between N and S is .5 Tesla (N=3T & S= 2.5T) and 1 complete rotation of the mechanism will result in a North to South change of -.5 Tesla followed by a South to North change of .5 Tesla, then do I understand correctly that ∆t would be the time required for 1/2 rotation?

 

[LeonhardEuler]

Yes, as long as the 3 and the 2.5 are in the same direction, otherwise $\Delta B$ is $3-(-2.5)=5.5T$

 

[GarageTinker]

Yes, as long as the 3 and the 2.5 are in the same direction, otherwise $\Delta B$ is $3-(-2.5)=5.5T$

When you say "in the same direction", I am understanding that you are referring to the movement of the magnetic field as being constant in one direction (i.e.) spinning clockwise and that the direction of the movement of the magnetic field does not change, i.e. flip-flopping clockwise/counter-clockwise?