A loop rotating in a magnetic field (How electric power generator works!)

[Fu-Kwun Hwang]

When a loop rotating in a uniform magnetic field.
The magnetic flux is changing which will induce electric field along the loop (produce voltage).
If the loop is rotating with constant angular velocity $omega$ . (The angle is $omega t$)
The magnetic flux in the loop will be $Psi =int vec{B}cdot dvec{A}= B A cos(omega t)$
So the induced emf $ = -frac {dPsi}{dt}=B A omega sin(omega t)$

The following simulation show how it works dynamically.
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So a loop rotating in a uniform magnetic field will generate electric power.
Reverse the process, a current in the uniform magnetic field will rotate (it become a motor).
Please check out Current Loop in magnetic field (How motor works!)

[Fu-Kwun Hwang]

Another similar one:

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[lookang]

When a loop rotating in a uniform magnetic field.
The magnetic flux is changing which will induce electric field along the loop (produce voltage).
If the loop is rotating with constant angular velocity $omega$ . (The angle is $omega t$)
The magnetic flux in the loop will be $Psi =int vec{B}cdot dvec{A}= B A cos(omega t)$
So the induced emf $ = -frac {dPsi}{dt}=B A omega sin(omega t)$

I suspect your model in the ejs codes is not reflecting the correct physics phenomena.
i change it to
"E0*cos(2*pi*x/(5*R))" for the Z in the analytic3D curve which symbolize the emf generated
and
E0*Math.cos(c2*pi2) for the Z in the emfparticle3D point which symbolize the instantaneous emf generated.
is my interpretation of the code in the model correct?

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Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
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[Fu-Kwun Hwang]

Assume the width and height of the loop are d and h.
The magnetic flux in the loop is $Psi =int vec{B}cdot dvec{A}= vec{B}cdot vec{A(t)} =B d h cosomega t$

So the induced emf $ epsilon= -frac {dPsi}{dt}=B (dh) omega sinomega t=BA_{max} omega sinomega t $

[lookang]

Assume the width and height of the loop are d and h.
The magnetic flux in the loop is $Psi =int vec{B}cdot dvec{A}= vec{B}cdot vec{A(t)} =B d h cosomega t$

So the induced emf $ epsilon= -frac {dPsi}{dt}=B (dh) omega sinomega t=BA_{max} omega sinomega t $

should be
is $Psi =int vec{B}cdot dvec{A}= vec{B}cdot vec{A(t)} =B d h sinomega t$
I check by sub t=0 ,  $Psi =0.
The initial condition is causing the error in your equation. Right ?

[Fu-Kwun Hwang]

Yes. There was a bug.
I am sorry that : I use different symbol in the simulation and in the web page.
The cta in EJS code was not the same $   heta$ in the above equation, and the direction for rotation was positive for colckwise rotation.

I have modified the whole code and change all the convention back to normal.

cta in the EJS code is the same as $   heta$ now (i.e. maximum area mean cta=0;)
THank you for the bug report. It is fixed and the first simulation has been updated!

P.S. another bug was fixed, too. (the check box for the Efield show be showE instead of showBF)