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Accelerating magnet and electromagnetic induction 
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#1
Oct208, 05:41 AM

P: 213

hi..i know the faraday's electromagnetic induction e=dФ/dt...supposing there is an coil of wire and i am accelerating magnet through the coil of wire and this will produce emf because accelerating magnet results in change in magnetic field...my question is how to relate this acceleration a and change in magnetic field dФ/dt...i think these two should be proportional...anybody help me..



#2
Oct208, 07:02 AM

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P: 12,070

You would have to know details of the magnet's field strength as a function of location.
As long as the magnet's field varies with position (i.e. is not constant), the magnet just has to be moving. It need not be accelerating. 


#3
Oct208, 08:36 AM

P: 213

e = ∂Ф/∂t α ∂v/∂t ∂Ф/∂t α ∂v/∂t is this correct?..do we have to introduce constant in the right hand side to make the two sides equal?.. 


#4
Oct208, 06:32 PM

Mentor
P: 12,070

Accelerating magnet and electromagnetic induction
No, not correct. It's proportional to v, not ∂v/∂t.



#5
Oct208, 08:52 PM

P: 213

Actually, e = ∂Ф/∂t α A(Acceleration) therefore, ∂Ф/∂t α ∂v/∂t [ A=∂v/∂t] How it is proportional to v?..it should be proportional to ∂v/∂t..if this is wrong,please give correct solution and also do we have to add constant to remove proportionality? 


#6
Oct208, 09:11 PM

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P: 12,070

I wonder if you are confusing something, either: A=acceleration vs. A=area of loop? v=velocity vs. v=voltage? The loop experiences a changing Bfield, which is dB/dt = (dB/dx) (dx/dt) Since v = dx/dt, there it is. Do you have a book to look at that explains induced emf? They usually have some sample problems involving moving loops or magnets. Acceleration never comes up. 


#7
Oct308, 06:57 AM

P: 213




#8
Oct308, 07:38 AM

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P: 12,070

I like the book Physics, by Douglas C. Giancoli. It's a noncalculus based textbook. I've seen it used for both AP high school physics, and college physics for nonphysics majors.
This stuff is in chapter 21 of the 5th edition. For $24, you can get a used, paperback copy from amazon.com  but this is a special edition that begins with Chapter 16. It contains all the electricity and magnetism chapters from the full book. http://www.amazon.com/gp/offerlisti...8/ref=dp_olp_2 Or, you could search on "induction" here: http://www.amazon.com/gp/reader/0130...pt#readerlink And start reading at p. 622 


#9
Oct308, 08:36 AM

P: 213

I understand this is the change in magnetic field for distance dx... is there any term for db/dx like v=dx/dt. 


#10
Oct308, 04:47 PM

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P: 12,070

Nope, just leave it as dB/dx. All it really says is B should not be constant (in space) in order to generate a change in flux this way.
A physics book will explain it much better, using figures, than I can. 


#11
Oct508, 05:14 AM

P: 213

I gone through "Electromagnetism and optics" An introductory course book. In that i find the motional emf which i was refering to. Below derivation was given there l and x are dimensions. i.e. l*x is area. Ф = Blx dФ = Bldx dФ = Blvdt dФ/dt = Blv e = Blv but this holds for only constant velocity i think...but what happens if we accelerate i.e. if the v is increasing. Even for increasing v also the magnetic field changes. does for increasing v also the above equation holds good? Or do i have to differentiate v again like this. d/dt (dФ/dt) = Bl dv/dt d²Ф/dt² = Bla . here a > acceleration. but e = dФ/dt and e != d²Ф/dt² what is this d²Ф/dt²? is this also changing magnetic field? i am going somewhere.help me.i think i am confusing you.what i want is.in the book it is given for constant velocity.can we use that for increasing or decreasing v also? if so,no problem. but if it is not,how to include that increasing or decreasing v? 


#12
Oct508, 05:29 AM

Sci Advisor
P: 8,636

Ф = Blx dФ/dt = d(Blx)/dt = Bl(dx/dt). In the last step, I assumed B and l were constant in this problem, and only x was changing. For a magnet moving at constant velocity or accelerating in some weird way, x will be a function of time, so we write it as x(t). You can find dx(t)/dt for any function x(t) you wish, and then find the corresponding dФ/dt. 


#13
Oct508, 06:57 AM

Mentor
P: 12,070

spidey, it works fine for when v is changing too.
e = Blv (in your example) still holds true. 


#14
Oct508, 09:09 AM

P: 213

Thank you Redbelly and atyy...i got it...i have another question...
Emf is generated in a wire when there is change in magnetic field..supposing i dont place any wire and i am changing magnetic field i.e. am moving or shaking magnet..now this is also changing magnetic field but there is no wire nearby,so where will the emf go or where is the electric field? is it in air? I understand the first equation for total flux of electric field ∫ E dA = (4∏ r²) * (Q /4∏e0 r²) = Q / e0 But I dont understand the maxwell's second equation∫ B dA = 0. we can also do derivation like for electric field. ∫ B dA = (4∏ r²) * (μ m/4∏ r²) = μm In the book, the derivation is not given and i couldnt find any derivation in websites also..all sites directly give this result...how maxwell derived this ∫ B dA = 0? 


#15
Oct508, 12:12 PM

Sci Advisor
P: 8,636

Roughly speaking, the LHS is an electric field, the RHS is charge, so it says a charge produces an electric field. Now if you place a positive and negative charge together, the RHS will be zero, and the total electric flux through any surface surrounding both of them will also be zero. So this equation requires that you can separate positive charge from negative charge. ∫ B dA = 0 Thinking in the same way, the above equation says that you cannot separate "positive magnetic charge" from "negative magnetic charge", all magnets always come with a north and south pole. If you cut the magnet into two pieces, you will generate two magnets, each with their own north and south poles. If we ever found a magnetic monopole, this equation would have to be modified. 


#16
Oct608, 07:59 AM

P: 213

i understand for flux of electric field. Are you saying since magnets come with north and south combined,there is no flux in closed surface? if there is no flux then it means that there is no magnetic field,isnt it? 


#17
Oct608, 01:44 PM

Sci Advisor
P: 8,636




#18
Oct708, 11:32 AM

P: 213




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