Question

Find the x-component of the electric field at the origin due to the full arc length for a charge of 4.5 µc and a radius of 0.55 m. the value of the coulomb constant is 8.98755 × 109 n · m 2 /c 2 . answer in units of n/c

Answer 1

Charge Q = 4.5 µc
 Radius of the arc R= 0.55 m
 Coulomb constant ke = 8.98755 Ă— 10^9 n • m 2 /c 2
 Charge per unit arc length = delta q / delta theta = Q / (pi / 2) = 2Q / pi
 => Delta q = (2Q / pi) delta theta
  So the x-component after subtitling the delta q is
 E = 2 ke Q / pi R^2 = (2 x 8.98755 Ă— 10^9 x 4.5 x 10^-6) / 3.14 x (0.55) ^2
 E = 80.89 x 10^3 / 0.94985 = 85.15 x 10^3 = 85151 N/C