1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Induced electric field

  1. Dec 11, 2012 #1
    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. jcsd
  3. Dec 11, 2012 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You can induce electric fields everywhere. Why do you expect that it would not be possible somewhere?
     
  4. Dec 12, 2012 #3

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You probably meant 'by a magnetic field, but not in the place where the magnetic field exists.

    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 'Aharonov-Bohm' effect.
     
    Last edited: Dec 12, 2012
  5. Dec 12, 2012 #4
    Yes. Say, for example, there's a long solenoid with a time-varying 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.
     
  6. Dec 12, 2012 #5

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Only in areas where there is a changing magnetic field.

    ∂B/∂t ≠ 0 implies that there is a magnetic field (apart from some specific points in time maybe).
     
  7. Dec 13, 2012 #6
    Take a circular area beyond the region of changing magnetic field,but it should include changing magnetic field area then
    E.2∏R=-∏r2.∂B/∂t,E is induced in region beyond WHERE B changes.
     
  8. Dec 13, 2012 #7

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    B= curl A. Apply Stokes' theorem for a B field in a solenoid.
    This gives an A outside the solenoid, where there is no B.
     
  9. Dec 13, 2012 #8

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I don't see how your quote and your post are related. You can get a non-zero 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.
     
  10. Dec 13, 2012 #9
    Yes, but only inside the solenoid. The electric field it produces also "exists" (is nonzero) outside the solenoid where B=0.
     
  11. Dec 13, 2012 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Sorry, but what you want just violates the laws of physics.

    $$curl(B)=\frac{1}{c}\frac{\partial E}{\partial t} + \frac{4\pi}{c} j$$
    You do not want currents and no magnetic field? => electric field is time-invariant. You cannot switch it on or off.

    This means that a time-independent charge distribution (which might consist of moving charges) is the only relevant option for a source of an electric field.
     
  12. Dec 13, 2012 #11
    No, it certainly doesn't. If there's a long solenoid of radius a and turn density n with a current I(t) running through it, it will induce a magnetic field B(t)=μ0nI(t) inside the solenoid. Outside of the solenoid B=0 everywhere.

    Evaluating the integral ∫E∙ds=-∂/∂t ∫B∙dA ⇔ E=-μ0na2 I'(t) / 2r

    Even though B=0 outside the solenoid, it still produces a nonzero E outside the solenoid.
     
  13. Dec 13, 2012 #12

    K^2

    User Avatar
    Science Advisor

    Transformers violate laws of physics? You learn something new every day!

    Sorry, I shouldn't be mean about it. It is a bit counter-intuitive. But yeah, if you take an infinitely-long 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 time-varying the current on the inner-solenoid. The B-field outside remains zero, but E-field is non-zero.

    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.)
     
  14. Dec 14, 2012 #13
    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.
     
  15. Dec 14, 2012 #14

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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.
     
  16. Dec 20, 2012 #15
    then..how will a time varying electric field induce magnetic field and where?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Induced electric field
  1. Induced Electric Field (Replies: 42)

  2. Induced electric fields (Replies: 10)

Loading...