Electric field and point charge problem

[zinedine_88]

Homework Statement

A particle with mass m and chare, q<0, moves in the field of a POINT charge Q>0, which is fixed in the origine of a cartesian coordinate system. The particle starts at REST in a distance R on the x-axis of a cartesian coordinate system : r(o)(vector) = Rix(vector), V(o) = 0

a) ... what is the force on the particle with charge "q" . Write down the equation of motion.

b) Show that the particle moves in a straight line along the x - axis!

C) prove the energy conservcation LAW :

[(m/2)(dx/dt)^2] + qQ / 4(pi)[E(not)]abs(x) = E = const!

d) how long does it take for the particle to reach the center ( where the charge Q sits)

Homework Equations

a) - i thing that the force is F = Qq/4(pi)(E(not)(R^2)times(-ix) unit vector , because it is moving from the right to the center... since Q is fixed! but tell me if i am right or wrong please..

b) I have no idea how to prove that mathematically...obviously there is no reason that q should move along the Y axis... but don't know what to do...

c) it says that i have to use the time derivative of the expression above and to use the equation of motion for x to show that it vanishes.. i don't get that HINT :( we have to assume that X is bigger than zero

d) says that i have to use the energy conservation law from part c...

there is nothing like that in our book...idk..

please help me

 

[Mindscrape]

b) Hello, you have a good start. You already showed that part b was true when you calculated the force. The force vector only has an x component, so the particle must only move along the x axis.

c) Remember that $F = m \frac{d^2 x}{dt^2}$. What did you get for part c as it is?

d) Yes, if you use energy conservation then you can figure out when the particles collide.