In a certain region of space, the electric potential is `V (x, y, z) = Axy - Bx^2 + Cy`, where A, B and C are positive constants.
(a) Calculate the x, y and z- components of the electric field.
(b) At which points is the electric field equal to zero?

Answer

A, B, C

Explanation

a. `E=-((delV)/(delx)hati+(delV)/(dely)hatj+(delV)/(delz)hatk)`
`=-[(Ay-2Bx)hati+(Ax+C)hatj]`
`=:. E_x=(-Ay+2Bx)`
and `E_y=(-Ax-C)`
(b)` E=0` if `E_x` and `E_y` are separately zero.
`:' -Ay+2Bx=0` ……..i
and `-Ax-C=0`……..ii
Solving these two equations
We get
`x=-C/A` and `y=-(2BC)/A^2`