we consider a uniform infinitely long line of negative charge. itslinear charge

Question

we consider a uniform infinitely long line of negative charge. itslinear charge density of - and is on the z axis. a smallpositive charge of mass m and a charge q is in circular orbit withradius R in the xy plane centered on the line of charge.
(a) derive an expression for the speed of the particle
(b) obtain an expression on the period of the particles orbit.


I think i am getting confused because i cannot seem to visualize ordraw what this system looks like. Also the axis and paths on theplanes are confusing to me.

the answers are (a) v= sqrt ( 2kq/m)
(b)T = pi*R*(sqrt(2m/kq))

Explanation / Answer

There is a vertical line of charge (negative). and a positivecharge that moves around that vertical line. Using Guass's law Q/0=E*S soE=Q/S0=l/2Rl0=/2R0 the centripitual force must be equal to the electric force. Eq=mv^2/r so q/2R0=mv^2/R v=sqrt(2kq/m) (1/40=k) b) the periodT=2R/v=2R/sqrt(2kq/m)=*R*sqrt(2m/kq)

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