A thin rod of length L carries a positive charge Q, which is uniformly distribut

Question

A thin rod of length L carries a positive charge Q, which is uniformly distributed along its length. (the rod is located along the negative side of the x axis starting at the origin.)
a.)write an integral expression that gives the x-component of the electric field at the point (x=a, y=0), where a>0. Your final answer should have x as the only variable of integration. Write your answer in terms answers in terms of (Q, L, a and the electric force constant k.)
b.) integrate the expression that you found and simplify.

Explanation / Answer

charge density = Q/L

consider a small lenght dx at a point -x

small charge in length dx = (Q/L)*dx

dEx = k*dq/(x+a)^2

dEx = k*Q*dx/L*(x+a)^2

dEx = (kQ/L)*(dx/(x+a)^2)

(b)

Ex = integral dEx

Ex = (kQ/L)*-(1/(x+a))   x = 0 to -L

Ex = (kQ/L)*( 1/a - 1/(a-L) )

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