Magnetic field created by accelerating charge?

[DangerRoss]

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EK content book states that magnetic filed is created by moving charge.
A solution to one of the EK 1001 questions states that EM wave is created by an accelerating charge. Isn't EM wave electric field+magnetic filed?

So which one is it? does a moving charge at constant velocity create magnetic filed, or should it be accelerating to create one? Can anyone please clarify? Thanks in advance.

 

[MD Odyssey]

You've asked a highly complicated question and I'll try to answer it as best I can.

Isn't EM wave electric field+magnetic filed?

It looks like you might have a subtle misunderstanding about EM waves, so let me start with a few simple definitions.

First, electric fields, which do not vary in time, are produced by charges - this is Gauss' law. It's described by the Coulomb potential. Magnetic fields, that also do not vary in time, are produced by DC currents. You have most likely seen this described using the Biot-Savart law. A simple example of an E-field source is a point charge, the square plate on a charged capacitor, etc. For B-fields, think of a DC current-carrying wire and note that a current is nothing more than a huge amount of charges all moving in the same direction at the same velocity.

It's important to recognize that the fields in these two examples are not changing in time, which is to say that the E and B fields are static. However, electromagnetic waves DO vary in time, thus for a simple current-carrying wire or a static charge distribution, no EM waves are produced. It's important to recognize what an EM wave is and what it isn't. EM waves are NOT simply E-fields plus B-fields; they are a specific oscillatory phenomenon.

Now, let's talk about how we generate EM waves. The Maxwell equations, which are usually beyond the scope of freshman physics, predict two things. First, time-varying electric fields produce time-varying magnetic fields. Additionally, time-varying magnetic fields produce time-varying electric fields. So, from this, you can see that generating either a time-dependent electric or magnetic field will yield an EM wave.

This is a highly simplified, and slightly inaccurate, summary of classical electrodynamics and I've omitted quite a bit, but the important parts are there. The key thing to remember is that electromagnetic waves are generated by time-varying electric or magnetic fields. Typically, most physicists tend to concentrate on the E-field in most situations and ignore the B-field when thinking about EM waves. But, you should know that either a time-varying E or B field is sufficient to generate the phenomenon we know as electromagnetic radiation. In practice, EM waves are generated using AC currents on wires which are proportional to the wavelength of oscillation. These are the basic mechanics behind how antennas work.

Now, to your questions:

Does a moving charge at constant velocity create a magnetic field?

Yup. This is the reason that a DC current-carrying wire creates a magnetic field.

Should it be accelerating to create one?

Yup. An accelerating charge creates a magnetic field as well.

Anyway, I hope that the earlier description helps, but if it doesn't, feel free to ask or PM me.

 

[DangerRoss]

This really helped. Thank you so much!

 

[MT Headed]

A charge moving at a constant velocity creates a constant magnetic field and no EM wave.

A charge with a changing velocity creates a changing magnetic field... a changing magnetic field creates a changing electric field... and a changing electric/magnetic field combo creates an electromagnetic wave.

Some common examples: an electron in simple harmonic motion sloshing back and forth along the length of a wire segment... well that's a radio antenna. Charged particles leaving radioactive material at high speed and then slowing down as they encounter cooling water will glow in the dark. Note that in both cases it takes acceleration to create an EM wave.

 

[MD Odyssey]

A charge moving at a constant velocity creates a constant magnetic field and no EM wave.

So, what happens if I put my coordinate system on the moving charge? It's now at rest in my reference frame, thus no magnetic field.

 

[MT Headed]

So, what happens if I put my coordinate system on the moving charge? It's now at rest in my reference frame, thus no magnetic field.

I actually asked this question in physics class, and the answer was some mumble about relativity and alternate universes and stuff. It is beyond the scope of MCAT physics. The fact that you noticed this anomaly means you will have no trouble with magnetism on the exam.

 

[MD Odyssey]

I actually asked this question in physics class, and the answer was some mumble about relativity and alternate universes and stuff. It is beyond the scope of MCAT physics. The fact that you noticed this anomaly means you will have no trouble with magnetism on the exam.

If your professor mumbled their way through it, they probably didn't understand it or remember. The normal interpretation doesn't invoke alternate universes (a phenomenon that is only accepted by a minority of physicists) but does involve special relativity.

The simplest way to understand it is to recall that there are four fundamental forces:

1. The gravitational,
2. The nuclear strong force,
3. The nuclear weak force, and
4. The electromagnetic force.

Notice that there is no electric or magnetic force - there is just the Electromagnetic Force. It turns out that in the context of special relativity, there isn't a strictly magnetic or electric field - both are components of a fundamental electromagnetic force and the force you see, electric or magnetic, is not a constant and, in general, will depend upon your reference frame.

A quote from Wikipedia summarizes this well:

According to the special theory of relativity, the partition of the electromagnetic force into separate electric and magnetic components is not fundamental, but varies with the observational frame of reference: An electric force perceived by one observer may be perceived by another (in a different frame of reference) as a magnetic force, or a mixture of electric and magnetic forces.
​

It's not intuitive but, like most anything in relativity, it can be understood with some rather gnarly mathematics, notably tensor calculus and differential geometry. Hopefully, my earlier comment helped put your mind at ease a bit. Too bad your physics professor ducked and ran when you asked the question.

 

[whiteshadodw]

A charge moving at a constant velocity creates a constant magnetic field and no EM wave.

A charge with a changing velocity creates a changing magnetic field... a changing magnetic field creates a changing electric field... and a changing electric/magnetic field combo creates an electromagnetic wave.

Some common examples: an electron in simple harmonic motion sloshing back and forth along the length of a wire segment... well that's a radio antenna. Charged particles leaving radioactive material at high speed and then slowing down as they encounter cooling water will glow in the dark. Note that in both cases it takes acceleration to create an EM wave.

a radio antenna is a little bit more complex than that. its actually an LRC circuit.

i think the main thing people should take away from this is that a charged particle with a given velocity can produce a magnetic field, and it can be acted upon by a magnetic field. any other information is beyond the scope of what is expected for the MCAT. just double check the AAMC topics list.

however, if people want to get into the details, then well, electrons, protons, etc when moving around do have wave properties. also, when a capacitor discharges to another capacitor, you can lose energy in the form of an EM wave. again though, i think that's beyond the scope of the MCAT and perhaps you're better off not needing it,

 

[MT Headed]

Hopefully, my earlier comment helped put your mind at ease a bit.

Okay, I have an MDOdyssey question then.

Let's say there are two long parallel wires, both with positive charge. Coulomb's law says they will repel each other.

Now let's say I get in my car and quickly drive between those wires. In my new frame of reference, I have parallel moving charges. The magnetic force (F=qvB) will cause the wires to be attracted to each other. If I drive fast enough, the magnetic force could even be larger than the electric force.

Do the wires bow out due to electric repulsion, or do they bow in due to current-induced magnetic attraction? Does the bowing depend on the frame of reference? In one frame of reference does the car get electrocuted, and simultaneously in the other frame of reference an observer standing outside the wires get electrocuted?

Inquiring minds want to know!

 

[MD Odyssey]

Okay, I have an MDOdyssey question then.

Let's say there are two long parallel wires, both with positive charge. Coulomb's law says they will repel each other.

Now let's say I get in my car and quickly drive between those wires. In my new frame of reference, I have parallel moving charges. The magnetic force (F=qvB) will cause the wires to be attracted to each other. If I drive fast enough, the magnetic force could even be larger than the electric force.

Do the wires bow out due to electric repulsion, or do they bow in due to current-induced magnetic attraction? Does the bowing depend on the frame of reference? In one frame of reference does the car get electrocuted, and simultaneously in the other frame of reference an observer standing outside the wires get electrocuted?

Inquiring minds want to know!

That's a really good question - I've never thought through this one before, but here's my best take on it.

Obviously, in the frame of the wires, the wires repel each other due to electrostatic repulsion and there are no magnetic fields.

Now lets look at the frame of the observer in the car. Each wire has a particular linear charge density and this charge density is in some way related to the magnetic field that the wires produce and it's also related to their electrostatic attraction. Because of something known as the Lorentz contraction, which causes distances to shrink due to the velocity of the observer, the perceived charge density in the two wires will increase, which alters the electric and magnetic fields seen by an observer in that frame. In particular, notice that if the charge density is increasing, then the electrostatic force also increases. This increase from what you would expect without accounting for relativistic effects is what counteracts the magnetic field produced by the movement of charge.

In both frames, the wires repel each other but the forces responsible for it, as perceived by observers in two different frames, are different. In one, it's purely electrostatic. In the other, it's a combination of electrostatic and magnetic forces.

I've never had a really great intuition for relativistic effects and I wouldn't be surprised if I've left out some important details - this is the best take on it that I can think of.