Question

If the potentail in the region of space around the point `(-1m,2m,3m)` is given by `V = (10 x^(2) + 5 y^(2) - 3 z^(2))`, calculate the three components of electric field at this point.

Answer 1

Correct Answer - `E_(x) = 20 V m^(-1) ; E_(y) = -20 V m^(-1) ; E_(z) = 18 V m^(-1)`
Here `x = -1 m, y = 2 m, z = 3m`
`E_(x) = (-del V)/(del x) = (-del)/(del x) (10 x^(2) + 5 y^(2) - 3z^(2))`
`= -20x = -20 (-1) = +- 20 Vm^(-1)`
`E_(y) = (-del V)/(del z) = - (del)/(del y) (10 x^(2) + 5 y^(2) - 3z^(2))`
`= -10y = -10(2) = -20 V m^(-1)`
`E_(z) = (-del V)/(del z) = -(del)/(del z) (10 x^(2) + 5 y^(2) - 3z^(2))`
`= 6z = 6 (3) = 18 Vm^(-1)`