Electromagnetism: Magnetic Fields

[SummerDawns]

Homework Statement

Two charged particles (P & Q) are fired into a uniform magnetic field that is directed into the page. When a particle possessing charge q moved through a magnetic field B at a velocity v it experienced the lorentz force that has a magnitude of F=qvB. What is the sign of P and Q.

The picture on the question looks similar to this just without the charges and P being the red line and Q being the blue,and the answer is the same as the picture.

Homework Equations

F=qvB

The Attempt at a Solution

I'm pretty sure you don't need to use the equation and I know the answer but I don't know how you come to the answer. I know you use the right hand rule and that the force on a negative and positive charge are in separate directions but I don't understand how you determine the charge of the particles.When I use the right hand palm rule, I have my palm facing up, my thumb to the right and the force pointing upwards. Is that right ? I don't think I'm applying the rules right because I think I've contradicted myself.

When I use the right hand grip rule for the red line, I have my thumb pointing to the left. Does that mean I is towards the left so the current is following to the left ? I don't think ti's right ? But I don't understand how knowing the direction of current will help me determine the charge of the particle. Thanks!

 

[BvU]

Hello Summer, welcome to PF :)

The equation is extremely useful for a whole lifetime if you keep it in mind as a vector equation$$\vec F = q\; \vec v\times\vec B$$I don't know if that helps you at the point where you are now, so I'll add some hands-on 'math'. The ##\times## indicates a vector product. There you need the right-hand rule.

Personally I prefer

## \vec x \times \vec y = \vec z ##:

For ##\vec x## use the thumb of your right hand. Let it point up.
For ##\vec y## use the index finger. Let it point forward, away from you
Then the direction in which the middle finger wants to point (your left) is the positive ##\vec z## direction. (*)​

(This is marked as the 'alternative' here)​

An alternative is the corkscrew rule.

## \vec x \times \vec y = \vec z ##:

turn ##\vec x## over the smallest angle towards ##\vec y##.
The direction in which the corkscrew (or any other normal screw) goes is the ##\vec z## direction.​

(*) Try it out with thumb to the right, B into the paper, hence middle finger upwards. It works: just like in your picture.

 

[gneill]

I'm pretty sure you don't need to use the equation and I know the answer but I don't know how you come to the answer. I know you use the right hand rule and that the force on a negative and positive charge are in separate directions but I don't understand how you determine the charge of the particles.When I use the right hand palm rule, I have my palm facing up, my thumb to the right and the force pointing upwards. Is that right ? I don't think I'm applying the rules right because I think I've contradicted myself.

For a moving positive charge: If you take your flat hand and align the fingers with the direction of the field and the thumb pointing in the direction of the particle motion, then your palm is facing the direction that the particle is pushed. Think of sweeping the particle aside with your palm). If the depicted motion is in the opposite direction then the charge must be negative instead.

If you know ahead of time that the moving particle is negative then you can use the left-hand version of the same rule.

When I use the right hand grip rule for the red line, I have my thumb pointing to the left. Does that mean I is towards the left so the current is following to the left ? I don't think ti's right ? But I don't understand how knowing the direction of current will help me determine the charge of the particle.

I presume that by the grip rule you are referring to how one determines the direction of the magnetic field caused by a current? The idea is to point your thumb in the direction of the current flow (charge motion) and then wrap your fingers around the conductor (or the line of the current if its just free particles moving through space). The direction that your fingers wrap will tell you the sense (direction of the arrows on the lines) of the circular field lines surrounding the current.

Note that for the problem in your post the field that's shown is not the field from the moving charge, but a field produced by some external source. So the grip rule is not the most direct way to get to the result. It requires require a bit of thinking about how magnetic fields interact.

When two magnetic fields (that is, from two different sources) try to occupy the same space, if they are both in the same direction so that their sum would increase the net magnitude of the field, then they will produce a repulsive force between the sources. If their sum would decrease the net field strength then their sources would be attracted to each other.

A way to remember this behavior is to think of space as "wanting" to dilute the magnetic field strength, pushing apart sources that would increase the field, and pulling together ones that reduce it. Of course it's entirely incorrect to anthropomorphize inanimate stuff in this fashion, but I find it a handy way to remember this detail: Space wants to be empty of magnetic fields.

Now, back to your moving charge. A current or moving charge produces its own magnetic field according to the grip rule. The field lines are in concentric circles surrounding the line of motion and the grip rule tells you their sense. Where these field lines are tangent to the external field they will either reinforce or cancel. If the field lines are in the same direction then a repulsive force occurs from that direction. If they are in opposite directions so that the net field is decreased then the particle is attracted in that direction.