Answer to Question #211964 in Electricity and Magnetism for Anita

Question

A potential field is given by V 5 3x2 y 2 yz. Which of the following is not true?

Answer 1

Gives

$V=3x^2y^2-yz$

$E=-\nabla V$

$E=-(\frac{dV}{dx}\hat{a_x}+\frac{dV}{dy}\hat{a_y}+\frac{dV}{dz}\hat{a_z})$

$E_x=-\frac{dV}{dx}=6xy^2$

$E_y=\frac{dV}{dy}=6x^2y-z$

$E_z=\frac{dV}{dz}=-y$

$$E=-(6xy^2\hat{a_x}+(6x^2y-z)\hat{a_y}-y\hat{a_z})$$