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19 September, 15:53

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.

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  1. 19 September, 16:23
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    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
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