Magnetic field of an infinite plane

[granpa]

what would the magnetic field of an infinite plane of current look like. its either zero or 1/d. I can't tell which.

all current in the same direction and entirely within the plane of course.

this is not homework unless self study is considered homework.

really, I want to understand why the external field of an infinite solenoid is zero.

 

[granpa]

well I'm quite sure it would be zero. I'm just not completely sure why

 

[Meir Achuz]

If the plane had a surface current density K then B=2pi K/c (in Gaussian units),
using Ampere's law. This result enters in the calculation of the reflection of a plane wave by a conductor.

 

[ibc]

If the plane had a surface current density K then B=2pi K/c (in Gaussian units),
using Ampere's law. This result enters in the calculation of the reflection of a plane wave by a conductor.

I got that too, from ampere's law, but wouldn't we expect the field to decrease when getting farther from the plane?

 

[Antenna Guy]

what would the magnetic field of an infinite plane of current look like.

It would look just like the electric field, but rotated 90deg (and 90deg out of phase). Think of a plane wave striking the plate - the magnetic field induces the current.

its either zero or 1/d. I can't tell which.

If you are only considering one direction (+z?), it is 1/d. If you consider both directions (+/-z), it is zero (because the magnetic fields in opposite directions would be 180deg out of phase). [correction: it would be 1/d for a finite plate]

I want to understand why the external field of an infinite solenoid is zero.

Similar to the above, but different.

but wouldn't we expect the field to decrease when getting farther from the plane?

No - because the infinite plate of uniform current has infinite gain perpendicular to the plate (all the energy is ratiated in a single direction).

Regards,

Bill

 

[ibc]

No - because the infinite plate of uniform current has infinite gain perpendicular to the plate (all the energy is ratiated in a single direction).

Regards,

Bill

the field is not infinite, and the gain of farther plane elements is decreasing to zero in infinity, so when you are farther away from the plane, each of these elements' field is smaller.
and it's not all in the same direction, as you get farther away (from the point at which you measure the field), the direction of the field is changing (of course when you go to the other side you get the same effect with opposite direction, so eventually the field is only in 1 direction parallel to the plane (perpendicular to the corrent), but a lot of the "energy" cancels out and don't contribute to the field.

 

[granpa]

looks like I totally missed the mark. so its constant. just like the field of an infinite plane of electric charge.

thanks for all the help