Two thin rods of length L lie along the x-axis, one between x = a and x = a + L, and the other between
x = –a and x = –a – L. Each rod has positive charge Q distributed uniformly along its length.
a. Calculate the electric field as a function of x produced by the rod on the left hand side
(from –a – L to –a) at points along the positive x-axis.
b. Determine the magnitude of the force that one rod exerts on the other.
E=∫[dq/4πε_naught*r^2] where dq=λdx for a line of charge
The Attempt at a Solution
Well since for part a, they only want the electric field in the positive x-axis I came up with:
E=∫from -a to -a-L of [λdx/4πε_naught*(-a-L+x)^2
E=L/2a+L(2a+2L) when the integral is evaluated from -a to -a-L. - I'm aware I need to multiply my constants back in but for right now, I'm just worried about the integral.
Am I on the right track?