Calculating magnetic flux of a rod

[yahelra]

Homework Statement

B = 0.02T
L = 40 cm
w = 10 rad/s
a: Electromotive force between O and C = ?

b: If electromotive force is the same - so what is the velocity?

I found 2 ways of solution. See "3. The Attempt at a Solution "

Homework Equations

φ = BA
ε = -dφ(t)/dt

The Attempt at a Solution

So I found 2 ways:
1. What every one would do - by Electric:

2. By the magnetic flux. But wait - There is no area.
So I found that if I would take in problem a the area of what the rod had passed (part of a disc) I would get the exact solution.

For problem b if I would take the area of a triangle I will get the solution too.My question - Why does the second way is also true? How can it be explained (For both problem a and b)?

Thanks a lot!

 

[TJGilb]

Is that a line or a rod? The way the picture is presented it doesn't look like there is any flux, let alone a change in flux. Did you give us the entire problem statement?

 

[yahelra]

I gave you the entire statement.
And you are right, as I wrote there are no magnetic flux because there is no area.

I meant that I've found that we can take an imaginary area and it will give us the same solution. ( See picture -0.016 V)

My questions are why is it true and how can it be explained?