## Induced electric field

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

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 Quote by 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.
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
$$\frac{\partial{\bf A}}{\partial t}$$ that can exist beyond the field, and induce an E field. This is like the 'Aharonov-Bohm' effect.

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## Induced electric field

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.

Mentor
 Quote by Meir Achuz A time varying magnetic field will have time varying vector potential $$\frac{\partial{\bf A}}{\partial t}$$ that can exist beyond the field, and induce an E field.
Only in areas where there is a changing magnetic field.

 Quote by elfmotat However, (assuming ∂B/∂t isn't zero) the electric field induced will also be nonzero outside of the solenoid.
∂B/∂t ≠ 0 implies that there is a magnetic field (apart from some specific points in time maybe).
 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.

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 Quote by mfb Only in areas where there is a changing magnetic field.
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.
 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.

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 Quote by mfb ∂B/∂t ≠ 0 implies that there is a magnetic field (apart from some specific points in time maybe).
Yes, but only inside the solenoid. The electric field it produces also "exists" (is nonzero) outside the solenoid where B=0.

Mentor
 Quote by elfmotat The electric field it produces also "exists" (is nonzero) outside the solenoid where B=0.
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.

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 Quote by 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.
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.

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 Quote by mfb Sorry, but what you want just violates the laws of physics.
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 $E = E_0\frac{\hat{\phi}}{r}$, $\nabla \cdot E = 0$ and $\nabla \times E = 0$ everywhere except r=0.)
 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.
 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.
 then..how will a time varying electric field induce magnetic field and where?