The electrical potential $V$ of a region of space is given by V(x, y,z)= A(x^2-3y^2+z^2) where A is a constant. a) Derive an expression for the electric field at any point in this region.
b) The work performed by the field when a test load of 1.50 μC moves from the point (x, y,z)=(0,0,0,250 m) to the origin is equal to 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 all planes parallel to the xz plane, the equipotential contours are circles.

e) What is the radius of the equipotential boundary corresponding to V = 1.280 V and y = 2.00 m?