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-component of the electric field. Express your answer in terms of the given quantities. b) Calculate the y-component of the electric field. Express your answer in terms of the given quantities. c) Calculate the z-component of the electric field. Express your answer in terms of the given quantities. d) At which point is the electric field equal to zero? 1-) x=0, y=0, z=0 2-) x=-C/A, y=0, z=-2BC/A^2 3-) x=-C/A, y=-2BC/A^2, z=C/A

a)  Eₓ = - A y + 2B x , b)  Ey = -Ax –C , c) Ez = 0 , d) The correct answer is 3

Explanation:

The electric field and the electric power are related

                    E = - dV / ds

a) Let's find the electric field on the x axis

                  Eₓ = - dV / dx

                  dV / dx = A y - B 2x

                  Eₓ = - A y + 2B x

b) calculate the electric field on the y-axis

                Ey = - dV / dy

                dV / dy = A x + C

                Ey = -Ax –C

c) the electric field on the z axis

              dv / dz = 0

              Ez = 0

.d) at which point the electric field is zero

Since the electric field is a vector quantity all components must be zero

X axis

              0 = = - A y + 2B x

              y = 2B / A x

Axis y

             0 = -Ax –C

              .x = -C / A

We substitute this value in the previous equation

             .y = 2B / A (-C / A)

             .y = 2 B C / A2

The correct answer is 3

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