The Attempt at a Solution
the electric field that Q is subjected to : E = q/(4piεor^2) ... i think
force that Q is subjected to :
i substitute k here for 1/(4piεo) to get F = (kQq)/(r^2)... i know the capital Q is supposed to be there, but don't know how it is fitted in algebraically.
then its just dotted into some angles for the vector math
r = √ (x^2 + a^2)
Force exerted on Q, F = (kQ|q|)/(x^2 + a^2) ( cosϑ i - sinϑ j ) + (kQ|-q|)/(x^2 + a^2) ( - cosϑ i - sinϑ j )
= -2(kQ|q|)/(x^2 + a^2) sin j = -2(kQ|q|)/(x^2 + a^2) * (a/√ (x^2 + a^2) )
work done in moving Q from (0,0) to (x,0)
not sure how to tackle this one.. I have an idea though W = ∫ F . dr or F . Δ r
can i just multiply my above result for the force into the change in x from the origin to where the point sits at (x,0)
something like (F . 0) + (F . x) ?
could someone give me a hand with what my start, i know the math looks a little shaky, but i think what i have up is very close to correct for the first two parts of the question.