CALC The electric potential V in a region of space is given by where A is a...

CALC The electric potential V in a region of space is given by

where A is a constant. (a) Derive an expression for the electric field at any point in this region. (b) The work done by the field when a 1.50-µC test charge moves from the point (x, y, z) = (0, 0, 0.250 m) to the origin is measured to be 6.00 X 10^-5 J. Determine A. (c) Determine the electric field at the point (0, 0, 0.250 m). (d) Show that in every plane parallel to the xz-plane the equipotential contours are circles. (e) What is the radius of the equipotential contour corresponding to V = 1280 V and y = 2.00 m?