What is the maximum induced EMF in a rotating contour near a straight wire?

[TSny]

There is no emf generated in the loop at either green dot.

In order for v x B to produce a nonzero emf in an element of length of the circuit, v x B must have a component parallel to the element of length. The emf of the entire loop is the integral of (v x B)$\cdot$ dl around the loop. For which sides of the loop is the dot product of (v x B) and dl nonzero?

 

[Ivan Antunovic]

There is no emf generated in the loop at either green dot.

In order for v x B to produce a nonzero emf in an element of length of the circuit, v x B must have a component parallel to the element of length. The emf of the entire loop is the integral of (v x B)$\cdot$ dl around the loop. For which sides of the loop is the dot product of (v x B) and dl nonzero?

Okay I just changed view a little bit , because I couldn't figure it out other way.

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Case one is when α = 0 ° , where I get e = 0 , which is very intuitive.
Case two is when α = 90 °, and since part 3 and 4 of contour don't contribute to the emf induced , I am only left with part 2 and 1 , and there (v x B) make angles 0 °and 180° , making it maximum. That way your idea?

 

[TSny]

OK, but for sides 1 and 2 isn't v x B opposite to dl for both of these sides?

 

[Ivan Antunovic]

OK, but for sides 1 and 2 isn't v x B opposite to dl for both of these sides?

Yes you are right for side 2 I took v from part 1 in my v x B.

One big thank you, sir @TSny !

After this conclusion , I am trying to derive to maximum emf induced with new approach , my first approach takes too much time (finding magnetic flux , taking derivative of flux as a function of time) , tried to find e1 , and since e max= 2 *e1 it's much easier to find the maximum emf induced, but messed something up with my integral after substitution for dl

EDIT:
I feel so stupid , every element dl has the same distance r from the center of rotation... r = a/2 and integral of dl gives AB = a,

therefore
e1 = μI/(4πa) * w * a/2 * a = μI/(4π) * w * a/2 = μI*w*a/(8π)
e = 2*e1 = (μI*w*a)/(4π) obviously wrong approach.

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