# [HELP] Confused about EMF induced in rotating coil

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:

rock.freak667
Homework Helper
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.

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.

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:
rock.freak667
Homework Helper
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.

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.

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:
rock.freak667
Homework Helper
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 .

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

rock.freak667
Homework Helper
Yup it makes sense. But equation-wise, subbing into the eqn you gave me E=-ωNBAsin(ωt), BA=0 isnt it?

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.

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

rock.freak667
Homework Helper
Ok, so NBA basically means the total maximum flux linkage to the coil (Constant), while the only thing that varies is the cos (wt)?

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