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. (use any variable or symbol stated above as necessary.) x-component ex, y-component ey, z-component ez. at what point electric field equal to zero.

E = (Ay-2Bx) i ^ + (Ax + C) j ^ + 0 k ^  and (-C / A i ^ + 2BC / A2 j ^)

Explanation:

The electric field the electric potential are related through the least gradient

           E = -ΔV = - dV / dx i^

Let's perform the calculations

        E = dB / dx i ^ + dV / d and j ^ + dV / dz k ^

        dv / dx = A and - B 2x

        dv / dy = Ax + C

        dv / dz = 0

        E = (Ay-2Bx) i ^ + (Ax + C) j ^ + 0 k ^

Where is E = 0

            Ex = 0

            Ay -2Bx = 0

            y = 2B / A X

            Ey = 0

            Ax + C =

            x = -C / A

           Ez = 0

For the total electric field to be steel the two components must be zero simultaneously

           y = 2B / A (-C / A)

          y = 2B C / A2

The coordinates of the point are (-C / A i ^ + 2BC / A2 j ^)

the answer is b ) square root of 5

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