You have two insulators. One is a straight line of charge, and the other is an arc of charge (a partial circle), as pictured above. The straight line of charge has uniform positive charge density λ₁ = A and is a distance d from point P. The arc on the right is centered at point P, has radius R and positive charge density λ₂= B and extends from θ= -Π/3 to Π/3

(a) Derive an expression for the electric field at point P due to the line of charge. Include both magnitude and direction. (Your answer should not include λ or x.)

(b) Derive all expression for the electric field at point P due to the arc of charge. Include both magnitude and direct ion. (Your answer should mu include λ or θ.)

(c) What is the total field at point P? (Note: if you did not get one of the previous answers use |E_line| = kA/L or |E_arc|=kB/2R)

(d) If R = L = d, for what ratio of A and B it is the electric field at point P=0 or is it never equal to 0?