What is the EMF generated in a Straight Conductor?

AI Thread Summary
The discussion revolves around calculating the electromotive force (EMF) generated in a straight conductor placed in a time-varying magnetic field. The participant attempts to use a transformer EMF formula, substituting a straight conductor for a coil, and expresses uncertainty about the correctness of their result. They seek clarification on the fundamental vector equation typically used for such calculations, noting that most resources focus on coils rather than straight conductors. The conversation highlights the confusion regarding the induced EMF in a straight conductor, particularly in relation to the absence of an enclosed area, and references a specific case from a file for further explanation. The need for accurate understanding of the principles governing EMF in varying magnetic fields is emphasized.
kpsr
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Homework Statement


What is the EMF generated in a straight conductor of length L placed in a time varying magnetic field B as
shown in the below figure..
Img_zps0twbecya.jpg


Homework Equations

The Attempt at a Solution


Time varying magnetic field is B.cosωt,
EMF = (d/dx)(B.L.cosωt) = -B.L.ω.cosωt
I don't know this result true or not Please correct me..
 
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kpsr said:

Homework Statement


What is the EMF generated in a straight conductor of length L placed in a time varying magnetic field B as
shown in the below figure..
Img_zps0twbecya.jpg


Homework Equations

The Attempt at a Solution


Time varying magnetic field is B.cosωt,
EMF = (d/dx)(B.L.cosωt) = -B.L.ω.cosωt
I don't know this result true or not Please correct me..
What is the original vector equation that is usually used to calculate this type of problem? :smile:
 
berkeman said:
What is the original vector equation that is usually used to calculate this type of problem? :smile:
In my above attempt I have used the transformer emf formula, in that formula I just used a straight conductor instead of a coil..
I saw that result in a website a long time ago and that site is not available right now. that's why i am not sure about the result.
 
kpsr said:
In my above attempt I have used the transformer emf formula, in that formula I just used a straight conductor instead of a coil..
I saw that result in a website a long time ago and that site is not available right now. that's why i am not sure about the result.
Assume that you just have a rod without a voltmeter. You have "Free" electrons inside the wire.
Okay so it is stationary right? What does that tell you about the forces acting on the electrons?
If I calculate the work done by these forces it is equal to the voltage so what do you find?Now let's say you want to check your results in a lab, You brought a voltmeter and connected it to the rod. Would you expect the result to be the same as the above? and Why? What law should you used here?
 
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kpsr said:
In my above attempt I have used the transformer emf formula, in that formula I just used a straight conductor instead of a coil..
I saw that result in a website a long time ago and that site is not available right now. that's why i am not sure about the result.
That is not the fundamental vector equation for this problem. If you are not familiar with that equation, it will take a bit more work to help you with this. What class is this for? What level in university or high school? :smile:
 
I have searched a lot, Please check the file from here ...
In this file Case(i) is the problem i mentioned in my post,
Please explain/elaborate Case(i) emf for me.
 
Last edited:
kpsr said:
Please explain/elaborate Case(i) emf for me.
Since this is a schoolwork-type question, our site rules require us to try to get you to figure it out on your own, rather than giving you the answer.
kpsr said:

The Attempt at a Solution


Time varying magnetic field is B.cosωt,
EMF = (d/dx)(B.L.cosωt) = -B.L.ω.cosωt
I don't know this result true or not Please correct me..
You didn't answer my question yet -- do you know the general vector equation that is used to calculate the EMF of a wire in a changing magnetic field? That is how you should approach this problem, rather than using simplifications of the equation like you posted above. If you're not sure which equation it is, just Google for calculate EMF in a wire from a changing magnetic field... :smile:
 
berkeman said:
You didn't answer my question yet -- do you know the general vector equation that is used to calculate the EMF of a wire in a changing magnetic field? That is how you should approach this problem, rather than using simplifications of the equation like you posted above. If you're not sure which equation it is, just Google for calculate EMF in a wire from a changing magnetic field... :smile:
I googled a lot and every time what i can found is the emf generated only for a conductor coil/loop in a changing magnetic field (B.cosωt),
and that general vector equation is
Emf_zpsbcl1aoox.jpg

or
Emf-1_zpsa2tcyajn.jpg

Here N is the number of turns in coil, A is the area of the coil and hence B.A is the flux Φ linked with that coil.
But what i am talking about a straight conductor with N almost 1 and there is no area A except length L.
that's why i replaced the flux BA from above equations with BL ,correct my approach...
 
kpsr said:
I googled a lot and every time what i can found is the emf generated only for a conductor coil/loop in a changing magnetic field (B.cosωt),
and that general vector equation is
Emf_zpsbcl1aoox.jpg

or
Emf-1_zpsa2tcyajn.jpg

Here N is the number of turns in coil, A is the area of the coil and hence B.A is the flux Φ linked with that coil.
But what i am talking about a straight conductor with N almost 1 and there is no area A except length L.
that's why i replaced the flux BA from above equations with BL ,correct my approach...
Good. So if there is no area enclosed, the induced EMF would be... :smile:
 
  • #10
berkeman said:
Good. So if there is no area enclosed, the induced EMF would be... :smile:
the induced EMF would be zero.. But that must be not correct, as from the working principle of transformers there must be an emf given by the Case(i) from the file or may be else, that what really confusing me, please clarify it..
 
  • #11
kpsr said:
the induced EMF would be zero.. But that must be not correct, as from the working principle of transformers there must be an emf given by the Case(i) from the file or may be else, that what really confusing me, please clarify it..
What is "Case(i)"? A transformer has an EMF induced by the changing magnetic field that pierces the coils because the coils have area. So the B dot dA term in the equation is non-zero...
Emf-1_zpsa2tcyajn.jpg
 
  • #12
berkeman said:
What is "Case(i)"? A transformer has an EMF induced by the changing magnetic field that pierces the coils because the coils have area. So the B dot dA term in the equation is non-zero...
Emf-1_zpsa2tcyajn.jpg
The Case(i) transformer Emf across a straight conductor of length L due to non-uniform magnetic field (B.cosωt) is
Emf-2_zps2se2jk72.jpg

Here also changing magnetic field (B.cosωt) pierces the straight conductor of length L, it's not a coil so there is only L in formula not area dA.
the above formula is not my own it's derived from this file here ...
my only question is that the result from the file is correct or not..?
 

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