# pset4 - APSC112 Problem Set 4 Useful Integrals(from...

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APSC112 Problem Set 4 Useful Integrals (from Information Sheets): Z dx ( x 2 + a 2 ) 1 / 2 = ln x + p x 2 + a 2 Z dx ( x 2 + a 2 ) 3 / 2 = 1 a 2 x ( x 2 + a 2 ) 1 / 2 Z xdx ( x 2 + a 2 ) 1 / 2 = p x 2 + a 2 Z xdx ( x 2 + a 2 ) 3 / 2 = - 1 ( x 2 + a 2 ) 1 / 2 1. How much work is required to assemble eight identical point charges, each of magnitude q , at the corners of a cube of side s ? Assume that initially the charges are separated by large distances from each other. 2. (Fig. 2) The charge configuration used in this problem is the same as that in Problem 1 of Problem Set 3. Four identical, positive point charges, each carrying charge Q are placed at the corners of a square side 2 L . The square lies in the XY -plane with its centre at the origin. Let P be a point on the Z -axis. (a) Determine the electric potential at P due to the four charges. (b) A point charge Q is placed at the point P 2 (0 , 0 , 2 L ) on the Z -axis and released, while the other four charges remain stationary. With what speed is it moving when it is infinitely far from the square?

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