Couple physics theory questions

[ptavasso]

Hi everyone. I have a few quick physics questions that aren't necessarily focused on what is tested on the MCAT, but more so for my understanding and curiosity. I understand the formulas and information required for the MCAT, but I would like to make sure that I have the correct fundamental knowledge behind this information.

 

1) since a changing electric field creates a magnetic field, then would all of the cases we're presented with that discuss a current moving in a circuit (as in a DC circuit) be creating a magnetic field? Please provide an example of when charge is not moving in an electric field (and thus B field is not created) since the examples I have encountered have been of a current moving in a circuit.

 

2) if what I have said in question 2 is all correct, would all circuits then be considered magnets since there is a current moving in the circuit, and this creates a B field? Or can you have a magnetic field without being a magnet? I understand the theory behind it, but I'm just curious then why a circuit isn't also considered a magnet since it has a magnetic field in the same way that a magnet has a magnetic field.

 

Thank you!

[MathToMed]

Unfortunately, this one is very abstract, and a bit technical.

 

Electric Fields and Magnetic Fields are entangled in a very deep way (so much so, that in some cases we simply refer to them as an "electromagnetic field"). To fully understand the behaviour, one must possess an understanding of Maxwell's Equations, which go far beyond the scope of the MCAT (in fact, just stating the formulas themselves requires intricate knowledge of Vector Calculus - http://en.wikipedia.org/wiki/Maxwell%27s_equations#Conventional_formulation_in_SI_units).

 

Unfortunately this leads to a bit of a wall - since I'm unsure of what your mathematical background is like, I may not be able to fully elucidate this entanglement...however, I can answer some of your questions:

 

A current moving through a wire in a DC circuit is no exception - it also creates a magnetic field! In fact, this principle is given a fancy name - Faraday's Law of Induction (http://en.wikipedia.org/wiki/Faraday's_law_of_induction) and serves as the theoretical framework for an electric motor/electric generator (which are like the opposite machines of each other - one uses energy stored in a voltage source to create a coordinated magnetic field and produce rotational motion, and the other uses rotational motion in a magnetic field to induce a current, which serves to store energy in a voltage source).

 

Note however that this also involves a lot of vector calculus, since it's the simplest necessary mathematical "language" used to describe the "flux" of charge across a theoretical surface (ie. how many electrons are passing through a hypothetical sphere around the wire, per second).

 

In regards to your question, I'm not sure I understand it - A charged particle will always create an electric field and always move in response to other electric fields. The only situation in which motion would not occur is if our universe was empty, save a single charged particle (but this is clearly not the case). This means the electrons in the atoms of your own body are themselves producing an electric field, and we are unable to isolate a single charge in a realistic way. (In theory we may be able to produce some sort of "box" around a single proton/electron, which cancelled out/dampened the effects of external electric fields, but this would fall outside any knowledge I have on the subject).

 

However, we can understand the field force(s) acting on a charged particle as follows: The "electric field" is like the component that is acting on the particle itself, regardless of its motion. The "magnetic field" is the component acting on the particle purely because of its motion.

 

If we dissect the formula F = q |v| |b| sin(theta), we can see that the force acting on a particle of charge q is dependent on:

 

1) the velocity, v

2) the component of the electric field that is not parallel to its velocity (bsin(theta))

 

Thus, if the particle were stationary (v=0, then |v| = 0, and so F = 0), no magnetic forces would be acting on it - it would be "immune" to any already existing magnetic fields, and it would not serve to amplify/dampen any of these fields (ie. it would not produce a magnetic field on its own).

 

We also know that if v and b were in the same direction (theta = 0 then sin(theta) = 0, hence F = 0 once again), no magnetic forces would be acting on it either...and it wouldn't produce a magnetic field on its own.

 

Note however that "in real life" these approximations are not sufficient... we would not be able to isolate a single magnetic/electric field to examine, and the actual electromagnetic forces acting on it would be a superposition of countless electric field components produced by the countless charged particles in the universe (albeit, each exerts a miniscule effect on its own, together they have the power to produce visible effects). So a particle may have no magnetic force as a result of it moving parallel to one electric field, but it is not moving parallel to a different one - and hence that field's force would still apply.

 

Regarding your 2nd question, it's all a matter of nomenclature - A "magnet" is, according to wikipedia's definition: a piece of iron (or an ore, alloy, or other material) that has its component atoms so ordered that the material exhibits properties of magnetism, such as attracting other iron-containing objects or aligning itself in an external magnetic field.

 

This is clearly something different from a DC circuit. If however, scientists chose to define a "magnet" as anything that produces a magnetic field, then a DC circuit would certainly fit that criteria, as would even the electrons in the atoms in our own bodies! We are in essence, very weak magnets, however the reason we aren't attracted to very powerful magnets is because of the chaotic nature of electron motion - essentially, all of the trillions upon trillions of electrons in our body are moving every which way, and through the law of large numbers, produce electric (hence magnetic) fields whose components cancel each other out. However in theory (very unlikely, but theoretical) the electrons may occasionally align themselves in such a way that we would actually exhibit an electric (hence magnetic) field, particularly when subjected to an external electric field. (Think of dipole moments)

 

Hope that helps - feel free to leave me a follow up if something is unclear.