Question

The electric potential is V= 5x − 3x^2y+2yz. Find the expressions for the x, y, and z components of the electric field over this region. What is the magnitude of the field at the point P that has coordinates (1, 0, -2) m?

Answer 1

• `bbE = ((-5x + 6x y ),(3x^2 -2z ),(- 2y ) )`

• `abs( bbE)_("(1,0,-2)") = sqrt(60)`

Explanation:

• Part 1

`bbE = - nabla V`

`= - ((del_x(5x − 3x^2y+2yz) ),(del_y(5x − 3x^2y+2yz) ),(del_z(5x − 3x^2y+2yz)) )`

`= ((-5 + 6x y ),(3x^2 -2z ),(- 2y ) )`

• Part2

`bbE(1,0,-2) = ((-5),(7),(0))`

`abs( bbE) = sqrt( (-5)^2 + 7^2 + 0^2 ) = sqrt(74)`