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Induced electric field 
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#1
Dec1112, 01:13 PM

P: 58

Can electric field be induced at a point near a time varying uniform magnetic field? "Near" means not the in the place where magnetic field exist. But at a point outside the field's presence.



#2
Dec1112, 05:03 PM

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P: 12,067

You can induce electric fields everywhere. Why do you expect that it would not be possible somewhere?



#3
Dec1212, 12:12 PM

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PF Gold
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A time varying magnetic field will have time varying vector potential [tex]\frac{\partial{\bf A}}{\partial t}[/tex] that can exist beyond the field, and induce an E field. This is like the 'AharonovBohm' effect. 


#4
Dec1212, 12:42 PM

P: 261

Induced electric field
Yes. Say, for example, there's a long solenoid with a timevarying current I(t) running through it. The resulting magnetic field is nonzero only inside the solenoid. However, (assuming ∂B/∂t isn't zero) the electric field induced will also be nonzero outside of the solenoid.



#5
Dec1212, 02:04 PM

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#6
Dec1312, 01:08 AM

P: 1,020

Take a circular area beyond the region of changing magnetic field,but it should include changing magnetic field area then
E.2∏R=∏r^{2}.∂B/∂t,E is induced in region beyond WHERE B changes. 


#7
Dec1312, 03:53 PM

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This gives an A outside the solenoid, where there is no B. 


#8
Dec1312, 03:59 PM

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P: 12,067

I don't see how your quote and your post are related. You can get a nonzero A everywhere if you like  even in a perfect vacuum, as you have gauge freedom. But you do not get an electric field without a changing magnetic field or some charge distribution.



#9
Dec1312, 04:24 PM

P: 261




#10
Dec1312, 04:47 PM

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P: 12,067

$$curl(B)=\frac{1}{c}\frac{\partial E}{\partial t} + \frac{4\pi}{c} j$$ You do not want currents and no magnetic field? => electric field is timeinvariant. You cannot switch it on or off. This means that a timeindependent charge distribution (which might consist of moving charges) is the only relevant option for a source of an electric field. 


#11
Dec1312, 05:56 PM

P: 261

Evaluating the integral ∫E∙ds=∂/∂t ∫B∙dA ⇔ E=μ_{0}na^{2} I'(t) / 2r Even though B=0 outside the solenoid, it still produces a nonzero E outside the solenoid. 


#12
Dec1312, 06:30 PM

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P: 2,470

Sorry, I shouldn't be mean about it. It is a bit counterintuitive. But yeah, if you take an infinitelylong solenoid, the magnetic field is ONLY present inside the solenoid. Yet you can wrap another solenoid around it, and induce a current on it by timevarying the current on the innersolenoid. The Bfield outside remains zero, but Efield is nonzero. This all has to do with curl of the electric field being governed by ∂B/∂t. Outside of the solenoid, both curl and divergence of E is zero, but it doesn't mean that the field itself is zero. Feel free to verify that circular E field with 1/R intensity satisfies conditions of both curl and divergence being zero. (In other words for [itex]E = E_0\frac{\hat{\phi}}{r}[/itex], [itex]\nabla \cdot E = 0[/itex] and [itex]\nabla \times E = 0[/itex] everywhere except r=0.) 


#13
Dec1412, 02:06 AM

P: 1,020

I have shown in post no.6 that even outside a solenoid if one take a circular area and if it encloses the region of changing magnetic field then electric field will be induced at far distances also.



#14
Dec1412, 07:50 AM

Mentor
P: 12,067

Ah ok, you are right. So we need a coil of infinite length, where B(t) changes linear in time. This gives a constant (in time), circular E(t) and no magnetic field outside.



#15
Dec2012, 09:35 AM

P: 58

then..how will a time varying electric field induce magnetic field and where?



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