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## Homework Statement

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 1.59x10

^{6}C

## Homework Equations

λ(the linear charge density) = q/l

The electric field E at a point due to one charge element carrying charge Δq =

(k

_{e}Δq)/r

^{2}

## 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 = ∫(k

_{e}λdx)/x

^{2}

Noting the constants, I moved them outside of the integral, and had:

E = k

_{e}λ∫dx/x

^{2}

Integrating, I got:

E = k

_{e}(Q/l) [ -1/x] evaluated from the lower limit .14m and the upper limit .43m.

E = k

_{e}(Q/l)[1/.14 - 1/.43]

Using all of that, however, gave me an answer of 6.8 x 10

^{6}, which is far off of the answer the book gave me, 1.59x 10

^{6}, 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.