Charge is uniformly distributed along the x axis with density ß. Use Gauss' Law to find the electric field it produces, and use this to calculate the work done on a charge Q that moves along the y axis from y = a to y = b.
Gauss' Law: e0 * electric flux = qencl
where e0 is epsilon0
The Attempt at a Solution
I thought dq = Bdx
q = B integral (x)
Then if we say EA = qencl/eo
where E is the electric field and A is the area
The areas wind up canceling and I got
E = B/e0
But I'm not sure that's right at all. Particularly since I can't see how I use this electric field to calculate the work done on a charge Q that moves along the x axis. Wouldn't I have to know if the charges were positive or negative? Because presumably opposite charges would cause the charge Q to speed up as it approaches the x axis while same would cause it to slow down... or am I on the wrong track completely?