A circular arc has a uniform linear charge density of 4 nC/m. 287 ◦ 2.5 m x y What is the magnitude of the electric field at the center of the circle along which the arc lies? The value of the Coulomb constant is 8.98755 * 109 N · m2 / C 2. Answer in units of N/C.

294.0724 N/C

Explanation:

From the question, we are given the following parameters: linear charge density,α = 4 nC/m = 4 * 10^9 C/m, radius, r = 2.5 m, the angle in the counter clockwise direction from the positive x-axis = θ = 287° and the Coulomb constant, Kc = 8.98755 * 109 N · m2 / C 2.

So, we can solve this question by using the formula below;

==>E (x direction) = - (Kc * α) / r * {sin 287° - sin 0°} i.

==>> - (8.98755 * 10^9 * 4 * 10^-9) / 2.5 * { - 0.9563047559630354

- 0} I.

==> - 14.4 * [-0.9563047559630354].

==> 13.8 N/C i.

E (y direction) = - (Kc * α) / r * (cos 0° - cos 287°) j.

==> - 14.4 * (1 - [ 0.29237170472273672]).

==> (-14.4 * 0.7076) j.

==> - 10.18944 n/C j.

==>E (x direction) ^2 + E (y direction) ^2.

==> (13.8^2 + ( - 10.18^2) N/C.

==> 190.44 N/C. + 103.6324 N/C.

= 294.0724 N/C