3. Find the gradient field F = Vy for the following potential functions 4: (a) 4(x, y ) = x2ytry2 ( 1) 4 ( 2 , y ) = Va2 + 2 2 (c) 4(2, y, z) = In(1+2+ 32+2 2) 4. Use Mathematica and the potential function in 3(a) to generate the following plots: (a) a contour plot of 4 on the square [-3, 3] x [-3, 3] (use ContourShading-False and Contours-40 or more in your image); (b) a vector plot of the gradient field you found in 3(a) on the same square (include PlotLegends-Automatic); (c) a stream plot of the gradient field you found in 3(a) on the same square; (d) a plot combining the graphs (a)-(c) together. Briefly discuss if everything looks good based on the theory discussed in class