Answer to Question #210672 in Electricity and Magnetism for Ali

Question

1) If a scalar field φ(x,y,z)=3x²y-y³z², calculate the gradient ∇φ at point M(1,-2,1).

Answer 1

$\varphi'_x=6xy,$

$\varphi'_y=3x^2-3y^2z^2,$

$\varphi'_z=-2y^3z,$

$\nabla \varphi=6xy\vec i+(3x^2-3y^2z^2)\vec j-2y^3z\vec k,$

$\nabla \varphi_M=-12\vec i-9\vec j-16\vec k.$