# Thread: Induced Electric Field

1. Assume we have a time changing magnetic field in some region of space. This will create an induced electric field. Maxwell's equations tell us this fact.

My question is...
As B changes with time, do the vectors that represent the induced electric field ever do something other than change in magnitude by a scalar?

I believe the vectors won't ever change in magnitude by a scalar if the induced electric field is created by a single resistive circuit loop. In this case, the B vectors at every point in space would grow in magnitude linearly with the current, but they would never do anything other than change in magnitude by a scalar, and the induced electric field would also change in magnitude by some scalar.

If there are multiple circuits driving some conductor system then B could change direction (i.e. rotate around) , and then the induced electric field vectors could change direction, move around, rotate, etc.

Hopefully I have explained this clearly.
Am I on the right track?  2.

3. Originally Posted by ScubaDiver
Assume we have a time changing magnetic field in some region of space. This will create an induced electric field. Maxwell's equations tell us this fact.

My question is...
As B changes with time, do the vectors that represent the induced electric field ever do something other than change in magnitude by a scalar?

I believe the vectors won't ever change in magnitude by a scalar if the induced electric field is created by a single resistive circuit loop. In this case, the B vectors at every point in space would grow in magnitude linearly with the current, but they would never do anything other than change in magnitude by a scalar, and the induced electric field would also change in magnitude by some scalar.

If there are multiple circuits driving some conductor system then B could change direction (i.e. rotate around) , and then the induced electric field vectors could change direction, move around, rotate, etc.

Hopefully I have explained this clearly.
Am I on the right track?
Your posts is extremely hard to follow. It would help a bit if you could be more precise in defining your geometry and the forcing functions you are considering, and defined very clearly what you mean by "change in magnitude by a scalar" (the same scalar at every point in space , which would violate the finite bspeed of light ?)

But I think it might help if you gave some thought to how a transmitting antenna works.  4. But I think it might help if you gave some thought to how a transmitting antenna works.
I have a basic understanding of what happens in a transmitting antenna. If there is an alternating current in the antenna, a changing magnetic field and induced electric field propagate away from the antenna at the speed of light. The induced e field and the magnetic field are perpendicular to eachother and 90 degrees out of phase. Also, the curl of the emitted e field is equal to . The differential form of Ampere's law tell us this.

What I am really trying to do is just visualize electric fields and how they change with time.

Consider two coils with different inductances. Imagine we put them in parallel and connect them to a battery. Initially, the current will be largest in the coil with the lower inductance. Then, the current will build up in the one with the larger inductance. What this means is that the induced electric field from this system will have a vector field where the vectors not only change in magnitude but also change direction. This is what I was trying to get at in my first post I guess.

defined very clearly what you mean by "change in magnitude by a scalar"
Like in the case of an eigenvector undergoing a linear transformation. I just mean that the vector don't ever rotate off their initial direction at all.  Bookmarks
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