pset3 - APSC112 Problem Set 3 Useful Integrals(from...

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APSC112 Problem Set 3 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. (Fig. 1) Four identical, positive point charges, each carrying charge Q = 3 . 0 nC, are placed at the corners of a square of side 2 L , where L = 10 cm. The square lies in the XY -plane with its centre at the origin. What would be the magnitude and direction of the resultant electric force on a point charge q = 2 . 0 nC if it were placed (a) at S , the midpoint of one of the four sides? (b) at a point P (0 , 0 , L ) on the Z -axis? 2. (Fig. 2) Positive point charges Q , 2 Q , 3 Q , . . . , 12 Q are affixed at the positions of the numbers 1, 2, 3, . . . , 12, respectively, on a circular clockface of radius R = 10 cm. If Q = 1 . 0 μ C, what is the electric field (magnitude and direction) at the centre of the circle? (Hint: Consider pairs of diametrically opposite charges. Determine the field due to each pair.) 3. (Fig. 3) A small sphere of mass 10 g is suspended by a light, insulating string between two large,
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