Question

Over a certain region of space, 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 = - bbnabla V`

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

`:. bbE = ((E_x),(E_y),(E_z))= - ( ( 5 − 6x y ),( − 3x^2 + 2 z ),( 2y ) )`

`bbE_( "(1, 0, -2)" ) = ( (- 5 ),( 7 ),( 0 ) )`

`implies abs( bbE_( "(1, 0, -2)" )) = sqrt74`