# What is the EMF generated in a Straight Conductor?

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1. Aug 25, 2016

### kpsr

1. The problem statement, all variables and given/known data
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..

2. Relevant equations

3. 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..

2. Aug 25, 2016

### Staff: Mentor

What is the original vector equation that is usually used to calculate this type of problem?

3. Aug 25, 2016

### kpsr

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.

4. Aug 26, 2016

### Biker

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 lets 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?

5. Aug 26, 2016

### Staff: Mentor

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?

6. Aug 26, 2016

### kpsr

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: Aug 26, 2016
7. Aug 27, 2016

### Staff: Mentor

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.
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...

8. Aug 28, 2016

### kpsr

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...

9. Aug 28, 2016

### Staff: Mentor

Good. So if there is no area enclosed, the induced EMF would be...

10. Aug 28, 2016

### kpsr

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. Aug 30, 2016

### Staff: Mentor

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...

12. Aug 31, 2016

### kpsr

The Case(i) transformer Emf across a straight conductor of length L due to non-uniform magnetic field (B.cosωt) is

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..?