Find the electric force vector on a particle of charge q located at the origin, which is also the center of curvature for a semicircular arc with radius w in the xy-plane that carries a uniform linear charge density lambda and exists only in the negative-x half of the plane. answer in terms of epsilon.
b. an annulus with inner radius w and outer radius 2w is located in the xy-plane, centered on the origin. it bears a uniform area charge density σ. at its exact center is a point charge q. find the resultant electric field vector on the z axis at z=3w. answer in terms of the permittivity.