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 a correct direction for the current and the current sign in the conductor. I am a bit lost in this one...
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!!!
0 answers