Point Charge and Infinite Wire

Jun 2014
1
0
Hello, I am new in this forum and I am having problems solving the following question:

Statement:

A long straight and thin wire has a charge Q per unit length. It is also carrying a current I. A point charge is moving with a velocity v parallel to the conductor, at a distance d from it. Find the velocity v, supposing the correct direction for the current and the charge density sign in the conductor.
My approach so far:

The electric field E at a distance d, generated by the conductor is:

E = lambda/(2*pi*d*e0) (where lambda is Q [c/m]

I assumed that the charge is positive, so the direction of the field pointing outwards the conductor.

The magnetic field generated by the current at a distance d from the conductor is:

B = u0*I/(2*pi*d)

If:
(x axis and y axis)
o -> Point charge Q

-------------- ->Conductor
-> I
So, the magnetic field is pointing out of the sheet and the electric force on the point charge Q is in the +y direction.

Using Newtons law, and assuming that the charge is moving parallel to the conductor:

Q*lambda/(2*pi*e0*d) - Q*v*u0*I/(2*pi*d) = 0

therefore, the charge's velocity is:

v = lambda/(e0*u0*I)

Is this correct or am I mistaken? Please Help!!!
 
May 2014
147
13
Poole, UK
A long straight and thin wire has a charge Q per unit length. It is also carrying a current I. A point charge is moving with a velocity v parallel to the conductor, at a distance d from it. Find the velocity v...
This doesn't sound right. If the wire is charged and there's no current, the charged particle will move away from it or towards it. It won't stay at a fixed distance from the wire. If the wire isn't charged but there is a current, the charged particle will move around the concentric magnetic field lines that surround the wire. When you combine these, the result isn't motion parallel to the conductor. Can you look at the problem afresh?