A rod 14.0 cm long is uniformly charged and has a total charge of -22.0μC. Determing (a) the magnitude and (b) the direction of the electric field along the axis of the rod at a point 36.0 cm from its center.
d (the distance between the center of the rod and the point) = .29m
l = length of the rod
The answer to part (a) is supposed to be 1.59x106C
λ(the linear charge density) = q/l
The electric field E at a point due to one charge element carrying charge Δq =
The Attempt at a Solution
At first I noticed that the distance between the end of the rod and the point should be .29m, as pointed out above. I assumed I could simply take the formula for the electric field and integrate it from 0 m to .29m, but when I did that it, well, didn't turn out too well.
Then I tried again, and instead integrated the formula over the distance of .14m to .43m. The process looked something like this:
E = ∫(keλdx)/x2
Noting the constants, I moved them outside of the integral, and had:
E = keλ∫dx/x2
Integrating, I got:
E = ke(Q/l) [ -1/x] evaluated from the lower limit .14m and the upper limit .43m.
E = ke(Q/l)[1/.14 - 1/.43]
Using all of that, however, gave me an answer of 6.8 x 106, which is far off of the answer the book gave me, 1.59x 106, and I'm not too sure my units would cancel out properly either.
Where exactly did I mess this thing up?
Thanks in advance for any help.