A potential field is given by V 5 3x2 y 2 yz. Which of the following is not true?
Gives
V=3x2y2−yzV=3x^2y^2-yzV=3x2y2−yz
E=−∇VE=-\nabla VE=−∇V
E=−(dVdxax^+dVdyay^+dVdzaz^)E=-(\frac{dV}{dx}\hat{a_x}+\frac{dV}{dy}\hat{a_y}+\frac{dV}{dz}\hat{a_z})E=−(dxdVax^+dydVay^+dzdVaz^)
Ex=−dVdx=6xy2E_x=-\frac{dV}{dx}=6xy^2Ex=−dxdV=6xy2
Ey=dVdy=6x2y−zE_y=\frac{dV}{dy}=6x^2y-zEy=dydV=6x2y−z
Ez=dVdz=−yE_z=\frac{dV}{dz}=-yEz=dzdV=−y
