Deriving Electric Field from Voltage

[Gear300]

This is probably more Calculus than it is physics. The voltage at a point X produced by a uniformly charged rod is V = (Ke*Q/l)*[ln(l+sqr(l^2+a^2))-ln(a)], in which point X is right above the left end of the rod by a distance a, l is the rod's length, Q is the charge of the rod, and Ke as the constant (sqr( ) refers to square root and ln is natural log).

X(point X a distance a from the left end of the rod, in which a is constant)


__________________ (uniformly charged rod)

I'm supposed to find the y-component of the Electric Field at X, in which I would just find the negative partial derivative of V in respect to y. Would that imply that I derive in respect to a? I've actually tried quite a number of derivations, but they always end up in something lengthy. The answer is Ey = Ke*Q/[a*sqr(l^2+a^2)].

 

[Shooting Star]

Would that imply that I derive in respect to a? I've actually tried quite a number of derivations, but they always end up in something lengthy. The answer is Ey = Ke*Q/[a*sqr(l^2+a^2)].

You are correct and so is the final answer. Try it once more. Remember, you have to differentiate wrt 'a' only. (There's a factor (l + sqrt(l^2+a^2) which cancels out.)