Chapter 23, Problem 23.78P

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

$\text{V}\left(\text{x},\text{y},\text{z}\right)=\text{A}\left({\text{x}}^2-3{\text{y}}^2+{\text{z}}^2\right)$

where A is a constant, (a) Derive an expression for the electric field $\stackrel{\to }{\text{E}}$ 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 × 10⁻⁵J. 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 arc circles, (e) What is the radius of the equipotential contour corresponding to V = 1280 V and y = 2.00 m?