# Why is there no magnetic field in a perfect conductor

1. Aug 12, 2010

### petergreat

In the treatment of waveguides, it's assumed that in a perfect conductor, both electric magnetic fields vanish. The first part is easy to understand because a non-zero electric field will cause the electrons to move. However why does the magnetic field also vanish?

2. Aug 13, 2010

### netheril96

Could you give the source?
It seems to me that only superconductors have the ability to expel magnetic field perfectly,called the Meissner effect

3. Aug 13, 2010

### petergreat

John David Jackson, Classical Electrodynamics, 3rd Edition, top of Page 353:
"Similarly, for time-varying magnetic fields, the surface charges move in response to tangential magnetic field ... to have zero magnetic field inside the perfect conductor."

This is one of the starting assumptions for the whole chapter on waveguides. The direct consequence is that the following boundary condition is assumed: the magnetic field near the boundary of the waveguide must be parallel to the boundary, i.e. have no normal component.

4. Aug 13, 2010

### Delta²

I think that the reason is that if there was time varying magnetic field normal component then there would be electric field but there isnt.

5. Aug 13, 2010

### petergreat

Thanks! That should've been obvious to me.

6. Aug 13, 2010

### Born2bwire

Yeah, this is only true for time-varying magnetic fields because in the case of time-varying fields it is always an electromagnetic field. The electric and magnetic components must exist together. In terms of statics, a magnetic field can exist in a perfect electrical conductor although I think one may argue that such a state is a bit ill-posed. When we talk about super conductors expelling magnetic fields, we actually impose extra conditions on Maxwell's Equations to do this. So that is why there is a conflict between what we say dealing with super conductors (real world PEC) and theoretical PEC.

7. Aug 14, 2010

Could you explain this a little more?

8. Aug 14, 2010

### Anamitra

Curl B=mu*epsilon[del_E/del_t] in the absence of free currents.If the electric field does not change curl B should be zero and hence B=constant. If B is zero for some instant it will remain zero for all other instants so long as del_E/del_t is zero.[David Griffiths--Introduction to Electrodynamics,Chapter 8 [Electromagnetic Waves]subsection,Guided waves,in a footnote]

Last edited: Aug 14, 2010
9. Aug 14, 2010

### Born2bwire

As Anamitra stated, Maxwell's Equations alone just stipulates that the magnetic field remains constant in a PEC with the value dependent upon the initial conditions. If we deal with a theoretical magnetostatic case then we can assume that the applied magnetic field will permeate the PEC. Obviously this really isn't possible in real life which is why I stated that this is a bit ill-posed. For a superconductor, take a look at the aforementioned Meissner effect. I do not have any references in on hand so perhaps another poster can give you the details, but the theory for superconductors presents stronger conditions on the magnetic fields inside the super conductor. Specifically, not only is an applied static magnetic field constant inside the material but it must be zero regardless of our initial conditions.

10. Aug 14, 2010

### Anamitra

It is true that in the classical sense if there is no change in the electric field the magnetic field should be constant.I have made this claim in my previous thread.But quantum mechanically there is a great problem since E and B are not good quantum numbers[they do not commute] and they follow the uncertainty principle.If E is zero, the uncertainty in E is zero and B can be anything!

11. Aug 14, 2010

### Acut

As already noted by previous posters, you may have a magnetic field inside a superconductor, but it can't change with time.

In fact, this is sometimes used to create very stable magnetic fields that last for months - thermal shielding isn't perfect so the superconductor will heat a bit and loose part of its superconducting properties, causing the magnetic field to vanish. But that is quite close to an ideal superconductor.