# Homework Help: [HELP] Confused about EMF induced in rotating coil

1. Aug 14, 2009

### qazxsw11111

Ok, now I got another question while doing electromagnetic induction questions.

I know flux linkage=NBA and in a rotating coil, Flux linkage=NBA cos wt, which differentiated (Faraday's Law) wrt time gives E=NBAw sin wt, where w = angular frequency.

However, when the plane of the coil is parallel to the magnetic field (assuming uniform magnetic field), NBA=0 since A=0. But according to E=BLV, where B, L and V are mutually perpendicular to each other, giving rise to a emf. But according to the differentiated eqn, NBA=0, so how can E be some value?

http://img27.imageshack.us/img27/5977/magneticij.png [Broken]

Vice versa when the plane is perpendicular to the field. NBA=maximum, but according to E=BLV, V and B are not perpendicular, giving rise to a zero emf.

Thanks.

Last edited by a moderator: May 4, 2017
2. Aug 14, 2009

### rock.freak667

well if it is rotating, at the point θ=0, then no emf is induced, but since it is rotating the momentum will cause it to move past θ=0 and thus cause an emf to still be induced.

When parallel to the magnetic field, no flux is cut, so no emf is induced.

3. Aug 15, 2009

### qazxsw11111

I knew that, but according to the graph in my lecture notes, flux is a cos function (eqn above). If you differentiate it, you will result in a sine curve, which at T/4 (initially coil plane is perpendicular to field), flux=0 but E=NBAw. My confusion is that I thought E at T/4 (Coil plane // to field) is 0.

Hope you understand what my confusion is all about. Anyone can help clarify this further?

Thanks.

Last edited: Aug 15, 2009
4. Aug 15, 2009

### rock.freak667

Φ=NBAcos(ωt)

E=dΦ/dt=-ωNBAsin(ωt) (-ve for opposite direction i.e. Lenz's law)

if E=0, then θ=π which corresponds to T/2, for t=T/4 i.e. θ=π/2, then the rate of flux cutting is maximum and E is maximum so E=ωNBA.

If you are still confused post your graphs and I'll see if I can explain it better for you.

5. Aug 15, 2009

### qazxsw11111

http://img228.imageshack.us/img228/6200/graphv.jpg [Broken]

Let T=period of rotation. Why NBA=0 but NBAw=max?

Last edited by a moderator: May 4, 2017
6. Aug 15, 2009

### rock.freak667

In your first graph, if you try to draw a tangent at the point where it crosses the axis, then the tangent is more or less vertical. So while the flux,Φ, is a minimum, it is the change in flux,dΦ/dt, that is maximum. Does it make a little more sense now?

Faraday's Law: The rate of change of magnetic flux is directly proportional to the emf induced. E=dΦ/dt .

7. Aug 15, 2009

### qazxsw11111

Yup it makes sense. But equation-wise, subbing into the eqn you gave me E=-ωNBAsin(ωt), BA=0 isnt it?

8. Aug 15, 2009

### rock.freak667

If you are thinking like that, then when Φ=0Wb , then the magnetic field cuts off and there is no emf induced!

In Φ=NBAcos(ωt), B and A are constant really.

9. Aug 15, 2009

### qazxsw11111

Ok, so NBA basically means the total maximum flux linkage to the coil (Constant), while the only thing that varies is the cos (wt)?

10. Aug 15, 2009

### rock.freak667

more or less because it is rotating so the only thing changing is the angle or wt as the case may be.