# Question about the Flux Rule

lugita15
The flux rule states that the emf induced in any loop is given by the rate of change of magnetic flux through that loop. In other words,$$\epsilon=-\frac{\partial}{\partial t}\int\int\vec{B}\cdot d\vec{A}.$$.
The thing that troubles me is the coincidence that the flux rule works in ALL cases. If a loop rotates at a constant angular velocity in the presence of a uniform constant magnetic field, the emf in the loop is given by the flux rule. If the magnitude of a uniform magnetic field perpendicular to a loop increases at a constant rate, the emf is still given by the flux rule. What is the connection between these four cases, that the flux rule works in all four?:
1. The circuit is stationary, and the magnetic flux increases (or decreases) due to a region of magnetic field moving into (or out of) the the area of the circuit.
2. The region of the magnetic field is stationary, and the magnetic flux increases (or decreases) due to (part of) the circuit moving moving into (or out of) a region of magnetic field.
3. There is a constant, uniform magnetic field, and the magnetic flux is sinusoidal due to the loop rotating with constant angular velocity.
4. The circuit is stationary, and the magnetic flux increases due to increase in the magnitude of the uniform magnetic field directed perpendicular to the circuit.
In all cases, emf=-(time derivative of magnetic flux).
Einstein famously proved in his "On the Electrodynamics of Moving Bodies," his first paper on the special theory of relativity, that due to the Lorentz transformations of the electric and magnetic fields, case 1 and case 2 are equivalent. How are case 3 and case 4 related to the each other, and to the first two cases?

Any help would be greatly appreciated.
P.S. One of the reasons I am asking this is that Feynman raises similar questions in his Lectures on Physics. He says in Volume II Page 17-2:
"We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena. Usually such a beautiful generalization is found to stem from a single deep underlying principle. Nevertheless, in this case there does not appear to be any such profound implication."

mr.survive
Very simple,
It is a general equation valid in all situations-Thia means there should be a general principle used for DERIVING this equation...INDEED IT IS THE CONSERVATION OF ENERGY(given by lenz's law) used...LETS SEE HOW.

We are interested to find INDUCED EMF,V...

Now V= work done on unit charge by magnetic force...

magnetic force =q(v.B.sinθ)

now , work done = F.dy = q(V.B.sinθ).dy

V= [q(v.B.sinθ).dy]/q

so,V=v.B.dy.sinθ.cosØ

now v=dx/dt

so,V=dx.dy.B.sinθ.cosØ/dt

V= -B.dA/dt = B.dA.(-cosω)/dt .... where [-cosω = sinθ.cosØ]

So.Mr.Feynman has said right about "DEEP UNDERLYNG PRINCIPLE"

i hope u will like it...and apply in all your situations undoubtfuly because it is derived from GENERAL LAW OF CONSERVATION OF ENERGY.....

lugita15
Very simple,
It is a general equation valid in all situations-Thia means there should be a general principle used for DERIVING this equation...INDEED IT IS THE CONSERVATION OF ENERGY(given by lenz's law) used...LETS SEE HOW.

We are interested to find INDUCED EMF,V...

Now V= work done on unit charge by magnetic force...

magnetic force =q(v.B.sinθ)

now , work done = F.dy = q(V.B.sinθ).dy

V= [q(v.B.sinθ).dy]/q

so,V=v.B.dy.sinθ.cosØ

now v=dx/dt

so,V=dx.dy.B.sinθ.cosØ/dt

V= -B.dA/dt = B.dA.(-cosω)/dt .... where [-cosω = sinθ.cosØ]

So.Mr.Feynman has said right about "DEEP UNDERLYNG PRINCIPLE"

i hope u will like it...and apply in all your situations undoubtfuly because it is derived from GENERAL LAW OF CONSERVATION OF ENERGY.....

Could you please elaborate on your response? I had some difficulty understanding the equations you wrote. If possible, could you use Latex to write the equations.

Any further help would be greatly appreciated.

pardesi
well time to bring in old topics
lugita hope u remeber our discussion and ofcourse we didn't reach any possible conclusion in our discussion here

well after lots of discussion finally i and my friends got http://www.mathlinks.ro/viewtopic.php?p=1036135#1036135 astounding( and i mean it) result!!!!
look at the last post of mine over there...if u have anything to add surely do it it's one of the most interesting things that i have seen in Electromagnetics.

Last edited:
lugita15
well time to bring in old topics
lugita hope u remeber our discussion and ofcourse we didn't reach any possible conclusion in our discussion here
Yes, that thread is precisely the reason I posted this question.

As to the other link you posted, I will have to examine it later in greater detail.