Question

the potential due to a point charge q at the origin may be written as v=q4πϵ0r=q4πϵ0x2+y2+z2√

Question 1 ;

The potential due to a point charge Q at the origin may be written as V=Q4πϵ0r=Q4πϵ0/√(x2+y2+z2)

Calculate Ex using equation Ex=−∂V/∂x.

Express your answer in terms of the given quantities and appropriate constants.

Part B

Calculate Ey using equation Ey=−∂V/∂y.

Express your answer in terms of the given quantities and appropriate constants.

Part C

Calculate Ez using equation Ez=−∂V/∂z.

Express your answer in terms of the given quantities and appropriate constants.

Part D

Show that the results of parts (a), (b), (c) agrees with the equation for the electric field of a point charge E⃗ =14πϵ0qr2r^.