Find the electric field (magnitude and direction) a distance z above the center of a square loop (side a) carrying uniform line charge lambda.

Find the electric field at a distance L directly above an infinitely large plane carrying uniform surface charge density Σ.

Shown in the figure below is a hollow disk of charge. The disk carries a charge density ? and has an inner radius R1 and an outer radius R2. You are to calculate the magnitude of the field at the point P which is a distance z above the plane of the disk. Determine the area element, dA =       Determine the charge element, dQ =       Determine the distance, s =       Determine the so-called, cos(?) =       Determine the integrand, ∬        Determine the lower bound of the ? integral:        Determine the upper bound of the ? integral:        Determine the lower bound of the r integral:        Determine the upper bound of the r integral:        Determine the final result of the integration:        NOTE: Please use k in your answers. Please do not use ?0.

Two spherical cavities, of radii a and b, are hollowed out from the interior of a (neutral) conducting sphere of radius R (see attatched image). At the center of each cavity a point charge is placed. Call these charges qa and qb. What is the field outside the conductor and what is the field within each cavity?