Induced electric field

dev70

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.

mfb

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

Meir Achuz

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.

elfmotat

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.

mfb

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).

andrien

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.

Meir Achuz

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.

mfb

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.

elfmotat

Yes, but only inside the solenoid. The electric field it produces also "exists" (is nonzero) outside the solenoid where B=0.

mfb

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.

elfmotat

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.

K^2

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.)

andrien

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.

mfb

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.

dev70

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