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!

When Magnetic field is suddenly switched off

  1. May 22, 2013 #1

    AGNuke

    User Avatar
    Gold Member

    A uniform non conducting ring of mass 1 kg, radius 1 m and having charge 1 mC distributed uniformly is free to rotate only about its central axis. Initially, a uniform magnetic field of 103 T is applied in a circular region of radius 0.5 m with centre on axis of ring. The ring was initially stationary. Now the magnetic field is suddenly switched off.

    Now, the angular speed of the ring just after switch-off the magnetic field is? (1/8 Rads/sec)

    I thought that since magnetic field is suddenly switched off, the flux (in the small circular region) would also become zero suddenly. So, in order to counter the change, the charged ring will rotate in such a manner so as to conserve the flux enclosed by the ring. ∴
    [tex]B_{initial}A_{region}=B_{ring}A_{ring}[/tex]
    [tex]10^3\times \pi(0.5)^2=\frac{\mu_0i}{2R}\times \pi(1)^2[/tex]
    [tex]i=\frac{dq}{dt}=\frac{Q}{2\pi R}\frac{Rd\theta}{dt}=\frac{Q\omega}{2\pi}[/tex]
    I must be going horrendously wrong somewhere because I am not even in remote to the options mentioned, let alone the answer. Please help. Seems like I am missing quite something I am unable to point myself at.
     
  2. jcsd
  3. May 22, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    There is no such law of nature. Consider the extreme case where the ring is very massive while the charge on the ring is infinitesimal. Could switching off the B field cause the ring to rotate fast enough to generate a flux that would equal the original flux?

    Faraday's law (or Lenz's law) implies only that the induced rotation of the ring will be in a direction such as to "oppose" the change in flux caused by switching off B. But "oppose" doesn't mean "maintain a constant value of flux".

    Think about what physical quantity acts on the ring to make it start to rotate. Can you think of a way to relate that physical quantity to the changing B field?
     
  4. May 22, 2013 #3

    AGNuke

    User Avatar
    Gold Member

    You mean to say I need something which can apply a Torque on the ring? Sorry to say but I am at my wits' end.

    UPDATE Are you implying Induced Electric field which is due to changed Magnetic field?
     
    Last edited: May 23, 2013
  5. May 23, 2013 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Yes.

    ehild
     
  6. May 23, 2013 #5

    AGNuke

    User Avatar
    Gold Member

    My Solution

    Alright. Let's see... I think I got it. Here it is:
    Induced Electric Field is given by:[tex]\oint \vec{E}.\mathrm{d}\vec{l}=-\frac{\mathrm{d} \Phi_B}{\mathrm{d} t}[/tex]
    [tex]\Rightarrow E.2\pi R=-\frac{dB\times \pi(R/2)^2}{dt}[/tex]
    Force on elemental charge on the ring will be tangential to the ring (since Electric field is also circular). Therefore, the Torque is given by[tex]\tau=\oint dq.\vec{E}\times \vec{R}\Rightarrow MR^2\alpha=EQR[/tex]
    [tex]\Rightarrow MR^2\int_{0}^{t}\alpha dt=-\int_{B}^{0} dB\frac{\pi R^2/4}{2\pi R}QR[/tex]
    [tex]\Rightarrow M\omega=\frac{1}{8}BQ[/tex]
    Now B = 103T, Q = 1 mC and M = 1 kg, the answer comes out to be 1/8 Rads/sec.

    I hope that this solution is correct.
     
  7. May 23, 2013 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It looks correct. Nice work!

    ehild
     
  8. May 23, 2013 #7

    AGNuke

    User Avatar
    Gold Member

    Never would had guessed about Induced Electric field if hadn't asked here. Each time I solve a question, I realize I need to know this and that. Someone really said, Increaseth knowledge, Increaseth Sorrow. (Now we are not supposed to be happy are we? :wink:)
     
  9. May 23, 2013 #8

    AGNuke

    User Avatar
    Gold Member

    Never would had guessed about Induced Electric field if hadn't asked here. Each time I solve a question, I realize I need to know this and that. Someone really said, Increaseth knowledge, Increaseth Sorrow. (Now we are not supposed to be happy are we? :wink:)
     
  10. May 23, 2013 #9

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Don't you feel happy when you understand something? That things happen in the way they should? That there are simple laws governing the Universe... :smile:

    ehild
     
  11. May 23, 2013 #10

    AGNuke

    User Avatar
    Gold Member

    I enjoy things at "my" pace and things at the moment are well beyond it. Like I was very amused to read about Quantum Physics, MWI and stuff, even though I didn't understood one bit of it.

    So right now, all that knowledge is pressing hard against me. There is happiness in discovering facts, but unhapiness over how less we know...:mad:
     
  12. May 23, 2013 #11

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You never can know everything. Enjoy what you know and be ready to learn new things.

    ehild
     
  13. May 23, 2013 #12
    I know that you are done with this thread but could you please tell me from where you got this equation? :)

    Thanks!
     
  14. May 23, 2013 #13
    What force would act on charge dq in field E? And what torque would it produce?
     
  15. May 23, 2013 #14
    ##dq \cdot E##? About CM of ring, it produces a torque of dqER. Looks like I got it. Thanks voko! :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted