# Induced electric field

1. Dec 11, 2012

### 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.

2. Dec 11, 2012

### Staff: Mentor

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

3. Dec 12, 2012

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

Last edited: Dec 12, 2012
4. Dec 12, 2012

### 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.

5. Dec 12, 2012

### 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).

6. Dec 13, 2012

### 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.

7. Dec 13, 2012

### 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.

8. Dec 13, 2012

### 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.

9. Dec 13, 2012

### elfmotat

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

10. Dec 13, 2012

### 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.

11. Dec 13, 2012

### 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.

12. Dec 13, 2012

### 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 $E = E_0\frac{\hat{\phi}}{r}$, $\nabla \cdot E = 0$ and $\nabla \times E = 0$ everywhere except r=0.)

13. Dec 14, 2012

### 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.

14. Dec 14, 2012

### 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.

15. Dec 20, 2012

### dev70

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