Magnetic Field through metal sheet

[sspitz]

Why does a metal sheet between two wires not have a shielding effect on the magnetic field? Considering the magnetic force can be explained as the electric field in a different frame.

With wires changing frames is a little complicated, but take this simplified situation. In the lab frame (L), there is a current carrying wire. Next to it a test charge is moving with speed v, parallel to the wire. Going to the frame of the test charge (F), I can use lorentz contraction to explain the magnetic force in L as an electric force in F. But what if I surround the test charge by a conductor? In L, the magnetic field should still act. In F, the electric field should be neutralized...

 

[cragar]

Good question. When you put the test charge inside a conductor the E field from the test charge will exist out side of the conducting box. And the E field from the wire will act on that. So the conducting box will move because of the E field from the wire. Just like if I have a metal sphere and I put an electron inside if it. The positive charges will be attracted to the electron inside and leave negative charges on the outside. The E field is zero inside the conductor but not outside or inside the box. At least that's what I think there might be more to it .

 

[sspitz]

Inside the conducting box the E field is zero. At least I know this for sure when the box is empty, so I assume if the test charge is small enough, it won't have an effect on the distribution of charge on the conductor.

If the test charge is large enough that it does have an effect, I don't know under what conditions E=0 inside the box. I asked that question around the same time, in fact, but no one answered. However, I think that is unrelated because we are using a test charge.

 

[sspitz]

Oh, by the way, I would just like thank you for replying. I had pretty much given up.

 

[cragar]

yes the E field is zero inside the conducting box if there is no charge in it. but if there is charge in it, then the E field is not zero. But with charge inside the box and an external E field the E field is zero inside the walls of the box. And also the charge inside the box will create charge separation on the conductor so that the E field will be zero. Now this separated charge is moving through space, so we have a sheet current and a B field. But I guess in the frame moving along with the electron there would not be a B field. just some stuff to think about.

 

[K^2]

Conductor doesn't block E-field. You can use Gauss Law to verify that, which is basically what cragar is getting at. Grounded conductor does block E-field, however, so it's still a good question.

Lets look at the surface charges that screen the E-field in moving coordinate frame. What do these look like in static frame? Well, these look like eddy currents. In fact, that's exactly them, and they will perfectly block the magnetic field. And if the material was a superconductor, the B-field would be permanently blocked, just like the E-field. However, conductor does have resistance, and eddy currents die. So if you go back to your moving frame, you'll find that the same thing should be happening. The reason surface charges can't block the E-field is because they would have to be moving relative to the conductor. That would require energy dissipation, however. So if you solve the problem for grounded conductor where surface charges are in rest with respect to conductor, you should see that the E-field cannot be blocked.