# Currents and magnetic fields

#### zzzzzz

Hello, I've just entered this forum and... the world of Physics. And I already have tremendous enigmas. Let's start with this.
Oersted revealed that a static magnetic field exists in the nearby of a current loop. Now "current" means "moving electric charges" and e.m. theory states that a moving charge generates a e.m. field. As a consequence, any current should be an e.m. waves generator (a transmitter), isn't it? If this is so, why are we able to detect only a static magnetic field in an Oersted-like experiment and not a varying magnetic field, along with its associated varying electric field, that again causes a magnetic field... in a word, what we call an e.m. wave?

I'm sure there's some basic idea in e.m. theory that I haven't really understood May anyone help me? Thanks.

#### Galileo

Homework Helper
A steady current (one that is constant in time) does not create a varying magnetic field and it takes a varying magnetic field to create an electric field. In a normal wire, you won't even notice an electric field, since, although charges are moving, the wire as a whole is electrically neutral. So the charge density needs to change with time in order to radiate em-waves. For example, if you run an AC current (AC is not a steady current) down a wire it radiates, this is simply how antenna's work.

Ah, and welcome to PF!

#### quasar987

Homework Helper
Gold Member
But what about the short interval between the time the curent "switch" is turned on and the time the curent has built itself up completely? During that time, the magnetic field changes very rapidly from 0 to its "steady curent value". And same thing when the curent is shut down.

Do these events send "cylindrical" E-M waves?

#### Galileo

Homework Helper
Yes, when you switch on the current, there is a magnetic field buildup, which creates an electric field that is opposed to the original one that started the current. This gives a sort of inertia-effect to current, it's sometimes called the back-emf and is proportional to the change in current. The actual constant of proportionality (called the self-inductance) depends on the configuration of your current loop. In a coil or solenoid this is relatively high, which is why it has a high impedance at high frequency AC current. When you switch off the current, there's an opposite effect which tends to continue the flow of the current.

There is a wave generated when you switch on the current, but the EM-waves generated in household current wires are relatively low though.

#### zzzzzz

Now, back to electromagnetics ‘cuase I think I’m making a mess ;p
I'm foreseeing a kind of dualism from what you say: while "steady" (not moving) charges generate static electric fields, steady currents generate static magnetic fields, and this has to be taken as a fact of Nature.
Now, how should I consider a single charge moving with constant velocity (in vacuum e.g.)? Along its path, charge density is not constant. Neither is the current flux in every point. The situation appears to me quite different from, e.g., the ideal one of a steady current along an infinite straight wire. In the latter case, there is a static magnetic field, while in the former there should be an electromagnetic field. Is this right or not?
Again, you say that a varying magnetic field (e.g. a moving magnet) has an electric field associated to it. Is this electric field static? Or a moving magnet becomes a source of e.m. radiation?

#### Galileo

Homework Helper
zzzzzz said:
Now, back to electromagnetics ‘cuase I think I’m making a mess ;p
I'm foreseeing a kind of dualism from what you say: while "steady" (not moving) charges generate static electric fields, steady currents generate static magnetic fields, and this has to be taken as a fact of Nature.
Instead of 'steady' charges, we speak of static charges. A static charge distribution gives rise to an electrostatic field. The precise mathematical statement of a static charge distribution is: $\frac{\partial}{\partial t} \rho(\vec r)=0$. (rho is the charge density).

Steady currents give rise to an magnetostatic field (some say 'static currents', which sounds like contradictio in terminis). The mathematical statement for steady currents is: $\vec \nabla \cdot \vec J(\vec r)=0$, where J is the current density.
This 'fact of Nature' can ofcourse be derived from Maxwell's equations.

Now, how should I consider a single charge moving with constant velocity (in vacuum e.g.)? Along its path, charge density is not constant. Neither is the current flux in every point. The situation appears to me quite different from, e.g., the ideal one of a steady current along an infinite straight wire. In the latter case, there is a static magnetic field, while in the former there should be an electromagnetic field. Is this right or not?
Yes, a single moving point charge does not consitute a steady current and it's electromagnetic field is relatively complicated compared to a steady current in a wire.
Again, you say that a varying magnetic field (e.g. a moving magnet) has an electric field associated to it. Is this electric field static? Or a moving magnet becomes a source of e.m. radiation?
If the bar is moving with constant velocity it will not radiate (it needs to accelerate for that), but is does have an electric field associated to it. You probably already know this, but when you move a bar magnet through a coil or metal ring, a current will run in the ring. It's this electric field associated with the bar magnet that pushes on the charges in the ring to make a current flow.

#### zzzzzz

Anyway, I think I have to think over them a little more. What I can’t really catch is the difference between the effects of a system moving with constant velocity (a steady flow of charges, a magnet moving with constant velocity...) and those of a system wich is somehow accellerated. I "understand" that it is all inside Maxwell’s equations, but I probably lack a visualization of these phenomena.

#### Galileo

Homework Helper
Well, there's a big physical difference between something that moves with constant velocity and something that is accelerating. As you probably know, whether you are moving with constant velocity or standing still cannot be felt or measured in any way. If you were in a big train with the windows painted black (so you can't look outside) and the rails is perfectly smooth (you can't hear the train either) there is no way you can know whether the train is moving or not. But when you accelerate, you can feel a jerk. If the train suddenly brakes you are thrown forward (relative to the train), if it turns left you bump into the right wall etc.
Because of this, if you know a static charge doesn't radiate, you can understand that one moving with constant velocity doesn't either.

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