A problem with a magnetic field and a revolving stick

• fara0815
In summary, the magnetic flux between the ends of a stick rotating around its center in a magnetic field is proportional to the emf generated by the motion. The EMF is 0.05 microVolts.
fara0815
Helle there!
Elektrodynamics is giving me a hard time. I have been trying to figure the following question out by using textkooks like Haliday, Schaum's Outline and even my professor's script ;)
But unfortunately, I do not know how to solve it.

Problem:

A stick of length 0,1 m is revolving around one of its ends in a constant magnetic field of B=(0;0;1) mT. The stick's angular velocity is $$\omega=(0;0;1) s^1$$.
What is the voltage between the two ends?
(5 microV).

Since I have absolutely no clue, I would appreciate if someone could give me a hint where to start and lead me in a few steps to the result.

Many thanks in advance to this great community!

You have probably already done the problem of finding the emf of a stick sliding on a rectangular loop of wire. Does that give you any ideas?

Let's see if I am getting close:

According to Faraday's Law, the magnetic flux is $$\phi_b= BA$$ when B is normal to the surface A.
My problem here is that I first have to get the surface which the magnetic lines go through.
l=length of the stick
The surface of one radiant is $$A_{rad}=\frac{\pi l^2}{2\pi}=\frac{l^2}{2}$$
with that I get the surface related to the time:
$$A(t)=\frac{l^2\omega t}{2}$$

So the magnetic flux is
$$\phi_B=\frac{ Bl^2\omega t}{2}$$

And the EMF is
$$U_{ind}=\frac{\delta}{\delta t}\frac{ Bl^2\omega t}{2}=\frac{ Bl^2\omega}{2}= 0.05 microVolts$$

What am I missing? Is this even close?

Last edited:
fara0815 said:
Let's see if I am getting close:

According to Faraday's Law, the magnetic flux is $$\phi_b= BA$$ when B is normal to the surface A.
My problem here is that I first have to get the surface which the magnetic lines go through.
l=length of the stick
The surface of one radiant is $$A_{rad}=\frac{\pi l^2}{2\pi}=\frac{l^2}{2}$$
with that I get the surface related to the time:
$$A(t)=\frac{l^2\omega t}{2}$$

So the magnetic flux is
$$\phi_B=\frac{ Bl^2\omegat}{2}$$

And the EMF is
$$U_{ind}=\frac{\delta}{\delta t}\frac{ Bl^2\omegat}{2}=\frac{ Bl^2\omega}{2}= 0.05 microVolts$$

What am I missing? Is this even close?
You are just missing the $\omega t$ in a couple of places (flux and derivative of flux) but you got it back in the end.

latex was leaving them out. Now they are there. Sorry about that ;)
and I got confused by the units. But thank you very much for your help!
I am soo glad I finally figured it out! Right in time for the class tomorrow morning ;)

What is the problem with a magnetic field and a revolving stick?

The problem is that the magnetic field can disrupt the rotation of the stick, causing it to wobble or even stop spinning altogether.

What causes this problem?

The problem is caused by the interaction between the magnetic field and the magnetic poles of the stick. When the stick is revolving, the magnetic poles are constantly changing position, which can disrupt the magnetic field and cause the stick to wobble or stop spinning.

What are the potential consequences of this problem?

The consequences can vary depending on the strength of the magnetic field and the material of the stick. In some cases, the stick may simply wobble or stop spinning, but in more extreme cases, the stick could break or cause damage to surrounding objects.

How can this problem be solved?

One solution is to shield the magnetic field by using materials that are not affected by magnetic fields. Another solution is to adjust the strength of the magnetic field or the speed of the revolving stick to minimize the interference.

Are there any real-life applications of this problem?

Yes, this problem can be seen in many everyday situations, such as with compasses and electronic devices. It is also an important consideration in industries that use rotating machinery, such as power plants and manufacturing plants.

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