# Magnetic Forces on charged particles

1. Apr 11, 2006

### 9danny

If a magnetic force does no work on a charged particle, how can it have any effect on the particle's motion?
Are there other examples of forces that do no work but have significant effect on a particle's motion?

2. Apr 11, 2006

### Hootenanny

Staff Emeritus
Centripetal force I believe does no work on the object.

The best explanation I can offer is the work done is defined as the product of the force and the distance moved in the direction of that force. Since both centripetal force and the magentic force is always perpendicular to the motion of the object, then no work can be done.

-Hoot

Last edited: Apr 11, 2006
3. Apr 11, 2006

### neutrino

9danny,
You might want to go through Girffiths' text where he gives an analogy with the normal force.

4. Apr 11, 2006

### nrqed

The concept of work is related to the concept of energy (theough the work energy theorem). If only one force is acting on an object, the work done by the force will give the change of kinetic energy. If there are several forces, you combine the work done by all of them.
The key point is that *energy* is a concept which does not contain all the information about the motion of an object. If you only know the kinetci energy of an object, say, you don't know anything about the direction in which it is moving. So there is *less* information in working with energy than in working with forces and with the actual motion. It's not as complete as knowing the initial position and velocity of an object and knowing all the forces acting on it at all points (in that case, everything can be calculated...at least classically). In using energy, one loses some information (for example, you can calculate what will be the speed of an object rolling down a roller coaster if you have the initial speed, height etc. but you cannot calculate the time it took).

So it is not surprising at all that a force which does no work on an object may still affect the motion of an object. Saying something about the work done by a force just gives partial information about the force involved and the motion.

The key point is that one could in principle solve everything with $\sum {\vec F} = m {\vec a}$ (classically) and never use the concept of energy. But using energy simplifies a lot of calculations, at the price of not saying everything about the motion of an object.

Any force which is perpendicular to the motion will do that, obviously. For example, if an object is attached to the end of a rope and swung around at uniform speed along a horizontal circle, the tension won't do any work. But the magnetic force is special in that it is *always* perpendiculat to the motion no matter what you do and this is quite special.

(As Hootenany said, any centripetal force has this property, but "centripetal force" is a generic term for whatever force acts toward the center of a circle in circular motion. It can be a tension, gravity, an electric force, etc. In that context, these forces do no work indeed. But the magnetic force is special in that it *never* do any work on a point charge)

Patrick

5. Apr 11, 2006

### nrqed

Do you mean the E&M book?
I hope that Griffiths does not say that the normal force never does any work!!! Because the normal force may do some work on an object!!

6. Apr 11, 2006

### neutrino

Yes, it's the E&M book. He does say that it does no work, the force being perpendicular to the displacement. But he also talks about the roles played by the two components when you're pushing something up a ramp with a purely horizontal force.

7. Apr 11, 2006

### nrqed

Ah ok. Thanks.
In that example (if the ramp is not accelerating itself!), the normal force does not do any work. But there are situations where the normal force does some work on an object. The most obvious example is an object resting on the floor of an elevator accelerating. Then the normal force does work on the object.