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

The x-component of the electric field at the origin due to a full circular arc with charge is zero because horizontal components from symmetrical points along the arc cancel each other out.

Step-by-step explanation:

To determine the x-component of the electric field at the origin due to a charged arc, one can use principles of electrostatics and symmetry. For a uniformly charged arc, the electric field components in the radial direction along the line of the arc cancel out due to symmetry, leaving only the horizontal components to consider. By integrating these horizontal components along the arc, one could find the total electric field. However, as the arc is a full circle, these horizontal components will cancel out due to symmetry, resulting in a net x-component of the electric field that is zero at the origin.

Answer 2

Charge Q = 4.5 µc
Radius of the arc R= 0.55 m
Coulomb constant ke = 8.98755 × 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