A particle of fluid is flowing in a wind tunnel where the velocity components are given by vx = U 1 + a 2 r 2 − 2a 2x 2 r 4 , vy = − 2U a2xy r 4 , vz = 0, where r 2 = x 2+y 2 and where U and a are given constants. A fixed electrical conductor on the z-axis creates the electrostatic potential field P given by P = A cos(qt) ln(x 2 + y 2 ), where A and q are constants. If the moving particle is at (a, a, 0) and t = t1, express the rate of change of P as seen by the particle at t1 in terms of the given quantities.