Force in a potential field V(x,y,z)

[amb123]

I have a problem that asks for force in the x-direction on a particle in a potential field given by some function V(x,y,z). The problem asks what the force in the x direction is if the particle starts resting at (1,2,3). I tried reviewing magnetism but found F = B x v where F and v are vectors representative of force and velocity respectively. However, am I to assume some velocity? If the problem is stated as previous am I to assume that it is at rest and that there would be no force if the velocity were zero? In a problem such as this do you assume the particle in question is charged?

I don't want to ask the specifics and give the function because I don't want is solved, but I just wan't to know where my thought processes are misleading me.
The problem also asks for the momentum 10s later, but since I'm having trouble relating force to potential field, I haven't started that part at all.

Thanks for any insight.
-A

 

[maverick280857]

Do you know that if a force field is conservative, it can be written in terms of a scalar function called the potential? (To be precise as the gradient of a scalar function)

Mathematically,

$\vec{F} = -\nabla V$

In Cartesian space, this is equivalent to the three scalar equations

$$F_{k} = -\frac{\partial V}{\partial x_{k}}$$

for k = 1, 2, 3

If you know the potential field, you know the force. If you know the force, you can probably do what you wanted to do.

If you are interested in the theory behind the very first equation of this post, then you might want to look up a text on vector calculus. (This: http://en.wikipedia.org/wiki/Gradient may be useful too).

 

[amb123]

Thanks! I will look into that, I remember gradients from a long time back, I was never terribly great with math and now it is all rusty.

Much appreciated,
-A