The discussion centers on calculating the electromotive force (EMF) generated in a straight conductor of length L placed in a time-varying magnetic field described by B.cos(ωt). The derived formula for EMF is EMF = -B.L.ω.cos(ωt), which is based on the transformer EMF formula. Participants emphasize the need for the correct vector equation for calculating EMF in a wire within a changing magnetic field, highlighting that the absence of an enclosed area results in zero induced EMF, which contradicts the principles of transformers.
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What is the original vector equation that is usually used to calculate this type of problem?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..
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..
In my above attempt I have used the transformer emf formula, in that formula I just used a straight conductor instead of a coil..berkeman said:What is the original vector equation that is usually used to calculate this type of problem?
Assume that you just have a rod without a voltmeter. You have "Free" electrons inside the wire.kpsr said:
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?kpsr said:
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:
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...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),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...
Good. So if there is no area enclosed, the induced EMF would be...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
or
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...
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..berkeman said:Good. So if there is no area enclosed, the induced EMF would be...
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...kpsr said:
The Case(i) transformer Emf across a straight conductor of length L due to non-uniform magnetic field (B.cosωt) isberkeman 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...
