Consider a large, thin, electrically neutral conducting plate in the xy-plane at z = 0 and a point charge q on the z-axis at distance z_charge = d. What is the electric field on and above the plate? Although the plate is neutral, electric forces from the point charge polarize the conducting plate and cause it to have some complex distribution of surface charge. The electric field and potential are then a superposition of fields and potentials due to the point charge and the plate’s surface charge. That’s complicated! However, it is shown in more advanced classes that the field and potential outside the plate (z ≥ 0) are exactly the same as the field and potential of the original charge q plus a “mirror image” charge –q located at z_image = -d.
a. Find an expression for the electric potential in the yz plane for z ≥ 0 (i.e., in the space above the plate).
b. We know that electric fields are perpendicular to conductors in electrostatic equilibrium, so the field at the surface of the plate has only a z-component. Find an expression for the field E_z on the surface of the plate (z = 0) as a function of distance y away from the z-axis.
c. A +10 nC point charge is 2.0 cm above a large conducting plate. What is the electric field strength at the surface of the plate

(i) Directly beneath the point charge

(ii) 2.0 cm away from being directly beneath the point charge?