modphysnoob Group Title EMF one year ago one year ago

1. modphysnoob Group Title

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2. modphysnoob Group Title

so we are supposed to find current in the loop assuming theere is a resistor there so I will start off with using magnetic force forumla q v X B but the book set it equal to Electric force

3. prakharluv Group Title

is there are any dimensions of loop?

4. Jemurray3 Group Title

The induced emf in the circuit will be (ignoring the minus sign for the moment) $EMF = \frac{d}{dt} \Phi_B = \frac{d}{dt} B\cdot A = B \cdot L \cdot \frac{dx}{dt} = BLv$

5. Jemurray3 Group Title

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6. Jemurray3 Group Title

But $EMF = BLv = IR$ so the current $I = \frac{BLv}{R}$

7. modphysnoob Group Title

I see, so there is no point to be messing around the force at all?

8. Jemurray3 Group Title

No, not really. What book is this?

9. modphysnoob Group Title

Fundamental of Applied Electromagnetics by ulaby

10. Jemurray3 Group Title

I am unfamiliar with it, sorry. I don't know, unless there's more to the question.

11. modphysnoob Group Title

I will attach that page

12. modphysnoob Group Title

13. prakharluv Group Title

ok for this loop,,, The magnetic flux linked with this loop will be, $\phi=Blx$ Since x is changing with time, the rate of change of flux $\phi$ will be induce emf given by : $e=\frac{ -d \phi }{dt }= \frac{ d }{ dt } Blx$ $e= -Bl \frac{ dx }{ dt }$ e=Blv

14. Jemurray3 Group Title

Oh, I see. What they are saying is the magnetic force on the particles is the same as if there was an electric field $\vec{E} = (\vec{v}\times \vec{B})$

15. modphysnoob Group Title

how did they come to that assumption?

16. modphysnoob Group Title

so magnetic field here would push all positive particle down , negative particle up , between them is potential difference

17. Jemurray3 Group Title

yes. And they didn't come to any assumptions, it's fairly clear. There is a force acting on them: $\vec{F} = q\vec{v}\times \vec{B}$ we know that for electric fields, $\vec{F} = q\vec{E}$ so our situation is just like what we would find if there happened to be an electric field present $\vec{E} = \vec{v}\times \vec{B}$

18. modphysnoob Group Title

I understand the formula , the part that confused me is why these two force must be equal

19. modphysnoob Group Title

oh, I think I understand , it is one force , not two force; we are just looking at it as if it two way

20. Jemurray3 Group Title

mhmm

21. modphysnoob Group Title

not quite?