Two arcs of charge are center at the origin. The arc at radius r has a linear charge density of +(lambda) while the arc of radius 2r has a linear charge density of -(lambda). (r = 5cm, lambda = 1nC/m, theta = 40°)
a) Calculate the magnitude and direction (as an angle from the x axis) of the electric field at the origin.
b) Calculate the electric potential at the origin.
c) Calculate the work done to bring +1 nC of charge from infinity to the origin.
d) Calculate the magnitude and direction of the electric force on +1 nC of charge when placed at the origin.
For A (I think) : Ey = 2kq/(pi)r^2
this is after I integrated from 0 to pi/2 with respect to theta[/B]
The Attempt at a Solution
Well the problem I am having is with this lambda. I calculated E(y) to be:
2kQ/pi(r)^2 where Q = 1x10^-9 and r = .05 m
With this I came up with 7192 n/c for the little arc and -719200 n/c for the larger arc. I then made the assumption that E(tot) = the addition of the smaller and larger arc which is:
726392 n/c @ 90° from the x axis
However I get the feeling that I cannot say Q = 1nC because its 1nC per m... I am not sure how to deal with lambda. I have only approached a so far because I am confused by lambda. I found similar problems and I could do this problem if I knew the total charge of the rod. Well I could do it for each arc individually, however the two combined has me a bit confused. I am not sure if I should add the respective E fields together or square them and take the square root of the product... any help would be appreciated.[/B]