1. The problem statement, all variables and given/known data A line charge has the total charge Q evenly distributed over a circle boat with radius a and sector 2β, placed according to the figure Find the Electric field E and the potential V in the origin. 2. Relevant equations I know for this case that E(r) = (1/4πε) ∫ (λ(r')/R2)R dl' , R is unit a vector λ(r') = Q/(2βa) R = - a *(cos(φ)x + sin(φ)y) dl'=a*dφ R2= a^2 V(r) = (1/4πε) ∫ (λ(r')/R) dl' 3. The attempt at a solution The electric field is not so hard to calculate I know E(r) =Q/(2βa)(1/4πε) ∫ ((-a *(cos(φ)x + sin(φ)y))/a3) adφ which is : (Q/8πεa2β) * [ -sinφx + cosφy] Now if I want to calculate the potential I know : V(r) = ∫ E*dl where dl = a*dφ*R = -a*dφ*(cos(φ)x + sin(φ)y) But I see (Q/8πεa2β) * [ -sinφx + cosφy] * (-a*dφ*(cos(φ)x + sin(φ)y)) = 0! And the real solution is : V(r) = (1/4πε) ∫ (λ(r')/R) dl' = (1/4πε) * (Q/2βa) ∫(adφ/a) and for a boat circle from π-β to π+β Or : What is actually wrong ?! If I do the same algorithm for a Sphere, it gives me a correct answer but why can't I do the same thing here through ∫ E*dl ?