# Is not possible the magnetic field to accelerate charges?

1. Oct 3, 2006

### mlazos

If we have a moving particle in a magnetic field the work of the magnetic field is always zero? Is not possible the magnetic field to accelerate charges?

2. Oct 3, 2006

### Staff: Mentor

A magnetic field cannot change the speed of a charged particle. It can change the particle's direction of motion, so it can change the particle's velocity, and in that way cause the particle to accelerate. Acceleration is the rate of change of velocity. Both acceleration and velocity are vector quantities and have direction as well as magnitide.

The classic example is uniform circular motion in which the particle's speed remains constant but its direction of motion continually changes, so that it is always accelerating towards the center of its circular path. This is in fact the path of a charged particle that moves perpendicularly to a uniform magnetic field, with no other forces acting on it.

3. Oct 3, 2006

### mlazos

Can you please be more precise? You say speed and velocity. They are the same things right? Imagine we have a particle with initial velocity that is moving toward a magnet (creates the magnetic field). Is it possible the magnetic field to accelerate the particle? The magnetic field can add to the kinetic energy or not? thanks for your time

4. Oct 3, 2006

### grant9076

The difference between speed and velocity is that speed has a direction component. The magnetic field changes the velocity by changing the direction only. In other words, the magnetic field can cause the particle to travel in circles instead of a straight line. This way it is constantly changing the direction (and hence the velocity) without changing the speed. I hope this helps.

5. Oct 3, 2006

an electron moving toward a magnet is another case, since if the electron moves toward the magnet, as he approaches the magnetic field grows, and changes direction, such things may cause a change in the energy of the electron...(or any other charged particle).

though if the magnetic field is constant in space, like inside a dense coil, is constant, an electron inside the coil's space will move in circles. the force will always be perpendicular to the velocity, so it will accelerate by changing it direction, but its absolute value will not change.
and energy is independent of direction of velocity, but by its absolute value. therefor constant magnetic field cannot change a particle's energy.

6. Oct 3, 2006

### mlazos

The magnetic field will rotate the particle so the particle will have rotational velocity. The total kinetic energy will increase right? can we say that at the end the particle is accelerated since the kinetic energy is growing?

7. Oct 3, 2006

### Staff: Mentor

A charged particle traveling perpendicular to a uniform magnetic field travels in a circular path at constant speed, therefore it has constant kinetic energy. Nevertheless, the magnetic force continuously causes the particle to accelerate via F = ma. This acceleration causes the particle's direction of motion to change continuously, but its speed remains constant.

When a particle accelerates, it changes its velocity. Velocity consists of a particle's speed together with its direction. Therefore, a change of velocity can mean a change in speed alone, or a change in direction alone, or a change in both speed and direction.

The magnetic force is always perpendicular to the particle's velocity, therefore it cannot change the particle's speed, only its direction.

8. Oct 3, 2006

### grant9076

I think and work better with analogies so hopefully this helps. If you are in a car going 60 mph in a straight line or 60 mph in a circle, you are still going 60 mph in either case. However, in the latter case (when you are traveling in a circle), you will feel a "force" that is pulling your body sideways. This "force" is the equal and opposite reaction to the lateral accelleration that is causing the circular path.

9. Oct 3, 2006

### mlazos

But what happens to the kinetic energy when the particle is not moving perpendicular but paraller to the magnetic field? The particle will get some torational velocity too that will be added to the total kinetic energy! right?

10. Oct 3, 2006

### grant9076

Actually, the speed will stay the same so the kinetic energy will also stay the same.

11. Oct 3, 2006

### grant9076

The reason is because in gaining the torsional velocity, some of the forward velocity (relative to the original axis) is lost.

12. Oct 3, 2006

### mlazos

the initial kinetic energy is $$E_{initial}=\frac{1}{2}mu^2$$ and the final energy will be $$E_{final}=\frac{1}{2}mu^2+\frac{1}{2}mu_{rotational}^2$$
so it will change and will increase right?

13. Oct 3, 2006

### grant9076

Actually, the kinetic energy that is added to the rotational component will be subtracted from the non-rotational component. That is why the overall speed (and kinetic energy) of the particle will stay the same.

14. Oct 3, 2006

### mlazos

So if the non rotational component will loose kinetic energy then will loose speed too!so the particle will somehow decelerate?

15. Oct 3, 2006

### Staff: Mentor

If the particle's velocity is parallel to the magnetic field, then the magnetic force on the particle is zero. In general, the magnitude of the magnetic force is

$$F_{mag} = q v B \sin \theta$$

where $\theta$ is the angle between the magnetic field and the particle's velocity. If the particle's velocity is parallel to the magnetic field, then $\theta = 0$ and therefore $F_{mag} = 0$ also.

Why do you think the particle will gain rotational velocity when there is no magnetic force acting on it?

16. Oct 3, 2006

### grant9076

Actually no. The gain in one will make up for the loss in the other. Its hard to come up with a spiral analogy so I will use the car analogy again. If you are traveling east at 60 mph (assume cartesian coordinates), your velocity to the east will be 60 mph and your velocity to the north will be zero. If you go around a 90 degree bend to the left at that same speed, you will end up going north at 60 mph while your velocity to the east will now be zero. The eastbound component of your velocity that was lost was gained by the northbound component of your velocity.

17. Oct 3, 2006

### mlazos

You are right. thanks for the answers people, i understood completely

18. Oct 3, 2006

### grant9076

Sorry, my last post was in response to mlazos. I was just slow posting it.

19. Oct 24, 2006

### M1keh

jtbell. Not you again ! :-)

I'm searching PhysicsForums for the answer to a question. You may be able to help ??

If you have two magnets ( no, nothing to do with relativity, I hope ), are the 'attractive' and 'repulsive' forces between the two magnets at the same distance equivalent or is there a difference between the two ?

ie. is A <---> B, the same size force as A >---< B ??

Probably not worded well, but do you see what I'm asking ?

Are the forces of magnetic attraction & magnetic repulsion exactly the same size. If you turn two magnets so that they attract each other x cm apart and then turn one around so that they repel each other x cm apart, are the forces equal is scale but opposite in direction ? Or is there a slight difference in the size of the forces ?

If one magnet is 10 time stronger than the other, are the attraction / repulsion the same not matter which way around the magnets are ? (Presumably, yes ?)

Have the relative strenghts of the attraction / repulsion ever been tested with very strong magnets ?

20. Oct 28, 2006

### quinn

A constant magnetic field can do no work on a charged particale.

HOWEVER, if the magnetic field changes one can do work on the charged particle,