# Homework Help: Against natural tendencies?

1. Mar 21, 2010

### DV10

1. The problem statement, all variables and given/known data

CONSIDER A SITUATION

AN ELECTRON SAY MOVING ON THE SCREEN OF UR COMPUTER FROM BOTTOM TO TOP . SUDDENLY A MAGNETIC FIELD IS SWITCHED ON OUTWARDS TOWARDS YOUR FACE FROM THE SCREEN . NOW VISUALISE THE MOTION OF ELECTRON SURELY A ANTI CLOCKWISE CIRCLE { AN ELECTRON IS NEGATIVELY CHARGED }

NOW CONSIDER THIS REVOLVING ELECTRON AS AN EFFECTIVE CURRENT LOOP IN THE SAME MAGNETIC FIELD . SO A LOOP WITH CLOCKWISE CURRENT & ABOVE SAID FIELD. NOW VISUALISE THE MAGNETIC MOMENT VECTOR OF THE LOOP & TO THE SURPRISE IT IS AT AN ANGLE OF 180(deegre) TO THE FIELD THE CONDITION OF UNSTABLE EQUILIBRIUM WITH MAXIMUM POTENTIAL ENERGY.

2. Relevant equations

3. The attempt at a solution
MY DOUBT IS AS THE SYSTEM HAS MOVED INTO THE CONDITION ITSELF THEN WHY IT MOVED TO MAX. ENERGY CONFIGURATION AND NOT TO MINIMUM ENERGY ONE . DISPUTING WITH ALL WE STUDY ABOUT THE NATURALBEHAVIOR OF SYSTEMS.

2. Mar 21, 2010

### gabbagabbahey

What makes you so certain that the system has moved to a higher energy configuration? When you speak of "the system", are you referring to just the moving electron, or are you also including the two magnetic fields present? Remember, the fields themselves can be thought of as carrying energy and are capable of transferring it to a dipole, much like a rocket engine transfers energy to a rocket.

In any case, a single electron moving subject to a magnetic field is a poor example. If you apply the Lorentz force Law to the electron, you will find the force on it will always be perpendicular to its motion, and hence no work will be done on it, and it's energy will not change.

3. Mar 21, 2010

### DV10

as far as i've read,potential energy of a current carrying loop in a uniform magnnetic field is U=-p.B
where p,B are magnetic dipole moment vector of the loop and the magnetic field vector(the field already present)
the tendency of a current carrying loop should have been to align itself WITH along the magnetic field already present..that would've been the min energy configuration..

4. Mar 21, 2010

### DV10

could you elaborate a bit on this?

5. Mar 21, 2010

### gabbagabbahey

There are two important reasons why you can't apply this formula blindly to a single electron moving in a circle subject to a magnetic field:

(1) The formula you give is only valid for current loops that are small enough to be approximately considered as pure magnetic dipoles.

(2) Current carrying loops typically contain a very large number of charged particles. Each of these particles will be accelerating (the direction of their velocity changes as they traverse the loop), and accelerating charges produce time-varying magnetic fields, which in turn induce electric fields (Faraday's Law). It is a straight-forward calculation to show that the magnetic fields never directly do any work on a charged particle, and hence the work in this case must come from the intermediary electric fields. When their are many moving charges, then each individual charge will produce an electric field that will do work on all other charges, but (according to Newton's 3rd Law) not on itself. When you add up all the forces from all the electric fields created by all the accelerating charges, you will find that $\textbf{F}=\nabla(\textbf{p}\cdot\textbf{B})$ and hence $U=-\textbf{p}\cdot\textbf{B}$, provided that the loop is closely approximated by a magnetic dipole. (This is the underlying mechanism as to how that equation is derived via the Lorentz Force Law)

For a single moving electron, their are no electric fields to do work on it. The only electric field present is the one it produces, which according to Newton's 3rd Law will do no work on it. (In fact, classical electrodynamics does predict that accelerating charges will exert a force on themselves. But, neglecting this so-called radiation reaction force, which violates Newton's 3rd Law, this is a valid argument).

For this reason, a single electron moving in a circle is a poor example, as its potential energy doesn't change.

A magnetic dipole would have a lower energy if it were aligned with the external field. However, this doesn't violate the laws of nature one bit.

A rocket ship has a lower energy sitting on the surface of Earth than it does in high orbit, does this mean that rocket ships violate the laws of nature? Of course not; the rockets engines burn fuel which provides additional energy to the rocket and raise it to a higher altitude.

So, a situation where you have a magnetic dipole anti-aligned with an external magnetic field must be similar to the rocket ship. If the dipole were created by the field, then its energy must have come from the field. Your particular example fails because a single electron in circular motion is not an ideal magnetic dipole, but if you were to devise some other scenario where an external field created a dipole that was opposed to the field, then you would have to conclude its energy came from the field (or rather, the power source that created the field) and was transferred to the charges that composed the dipole via intermediary induced electric fields.

If you are curious as to how to find the energy stored "in a magnetic field", look up Poynting's theorem.

6. Mar 22, 2010

### DV10

how do you define an idealistic situation here?i mean,lets say instead of a single electron, i have a beam of electrons..doesnt that work as a better approxiamtion?
in that case doesnt your 2nd arguement fail?
as much as i've infered from this discussion is, that basically are you trying to say that in the scenario i've presented,an external agency has to do work on the system in order to sustain the uniformity of the magnetic field?(by uniformity i mean keeping the configuration of the field from changing)(this is the only seemingly valid arguement here)

ps-i appreciate your time here,thanks for trying to clear things up.. but im still a bit confused here..