2. (15) Method of images I The figure on the left shows a head-on view of a right-angled corner formed by two grounded, conducting plates and a positive point charge

+q a perpendicular distance a from both conductors. The figure on the right shows the charge/image system for this problem (this is a 3-dimensional problem; the z-axis is coming out of the plane of the page). (a) A few qualitative questions that can be answered without calculations:i. What is the sign of the charge induced on the conductor?ii. What is the direction of the electric field on (just above) the lower surface(y = 0, x > 0)?iii. What is the electric field at the origin?iv. What is the limit of the induced surface charge on the lower surface (y = 0,x > 0) as x → 0 ? (b) Calculate the surface charge o(x, z) induced on the lower surface.(c) Calculate the net force on the point charge q.

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