When Magnetic field is suddenly switched off

1. May 22, 2013

AGNuke

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. ∴
$$B_{initial}A_{region}=B_{ring}A_{ring}$$
$$10^3\times \pi(0.5)^2=\frac{\mu_0i}{2R}\times \pi(1)^2$$
$$i=\frac{dq}{dt}=\frac{Q}{2\pi R}\frac{Rd\theta}{dt}=\frac{Q\omega}{2\pi}$$
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. May 22, 2013

TSny

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?

3. May 22, 2013

AGNuke

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
4. May 23, 2013

ehild

Yes.

ehild

5. May 23, 2013

AGNuke

My Solution

Alright. Let's see... I think I got it. Here it is:
Induced Electric Field is given by:$$\oint \vec{E}.\mathrm{d}\vec{l}=-\frac{\mathrm{d} \Phi_B}{\mathrm{d} t}$$
$$\Rightarrow E.2\pi R=-\frac{dB\times \pi(R/2)^2}{dt}$$
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$$\tau=\oint dq.\vec{E}\times \vec{R}\Rightarrow MR^2\alpha=EQR$$
$$\Rightarrow MR^2\int_{0}^{t}\alpha dt=-\int_{B}^{0} dB\frac{\pi R^2/4}{2\pi R}QR$$
$$\Rightarrow M\omega=\frac{1}{8}BQ$$
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.

6. May 23, 2013

ehild

It looks correct. Nice work!

ehild

7. May 23, 2013

AGNuke

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? )

8. May 23, 2013

AGNuke

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? )

9. May 23, 2013

ehild

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...

ehild

10. May 23, 2013

AGNuke

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...

11. May 23, 2013

ehild

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

ehild

12. May 23, 2013

Saitama

I know that you are done with this thread but could you please tell me from where you got this equation? :)

Thanks!

13. May 23, 2013

voko

What force would act on charge dq in field E? And what torque would it produce?

14. May 23, 2013

Saitama

$dq \cdot E$? About CM of ring, it produces a torque of dqER. Looks like I got it. Thanks voko!