**Question:**

A point charge q is brought to a position a distance d away from an infinite plane conductor held at zero potential. Using the method of images, find:**(a)** The surface-charge density induced on the plane, and plot it.**(b)** The force between the plane and the charge by using Coulomb’s law for the force between the charge and its image.**(c)** The total force acting on the plane by integrating σ^{2}/2ε_{0} over the whole plane.**(d)** The work necessary to remove the charge q from its position to infinity.**(e)** The potential energy between the charge q and its image [compare the answer to part d and discuss].**(f)** Find the answer to part d in electron volts for an electron originally one angstrom from the surface.

**Solution: **

(a) By assuming a cartesian coordinate system with x and y axes on conductor plane and z-axis perpendicular to the conductor plane where the point charge and its image are on the z-axis, any arbitrary point p in space with position vector r , is at distances r_{1} and r_{2} from the point charge and its image respectively, as it is represented in figure (1).

Electric field at point p is given by,

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