The electirc potential at a point `(x, y, z)` is given by `V = -x^(2)y

1.	The electirc potential at a point `(x, y, z)` is given by `V = -x^(2)y - xz^(3) + 4` The electric field `vecE` at that point isA. `vecE = hati (2xy +z^(3)) + hatj x^(2) + hatk 3xz^(2)`B. `vecE = hati 2xy + hatj (x^(2) + y^(2)) + hatk (3xz - y^(2))`C. `vecE = hati z^(3) + hatj xyz + hatk z^(2)`D. `vecE = hati (2xy - z^(3)) + hatj xy^(2) + hatk 3z^(2) x`
Answer» Correct Answer - A Electric field at a point is equal to the negative gradient of the electrostatic potential at that point. Potential gradient relates with electric field according to the following relation `E = (-dV)/(dr)` `vecE = - (delV)/(delx) = [-(delV)/(delx)hati - (delV)/(dely) hatj - (delV)/(delx)hatk]` `= [hati (2xy + z^(3))+ hatj x^(2) + hatk 3xz^(2)]`

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