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2061x1_solutions_sp02

# 2061x1_solutions_sp02 - PHY2061 R D Field PHY 2061 Exam 1...

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PHY2061 R. D. Field Exam 1 Solutions Page 1 of 10 February 12, 2002 PHY 2061 Exam 1 Solutions Problem 1 (10 points): Circle true or false for following (1 point each). (a) (True or False) Gravity is much stronger than the electrostatic force. (b) (True or False) Electric field line do not begin or end in charge-free regions (except at °infinity±). (c) (True or False) Where electric field lines are dense the electric field is weak. (d) (True or False) An electric dipole produces an electric field that is not zero anywhere except at °infinity±. (e) (True or False) Two positive point charges separated by a distance d produce an electric field that is not zero anywhere except at °infinity±. (f) (True or False) A uniform infinite sheet of charge produces an electric field that has the same magnitude everywhere in space. (g) (True or False) The vector function y x x y y x E ² ² ) , ( = r represents a possible electrostatic field with magnitude given by 2 2 ) , ( y x y x E + = . Note that 0 ² 2 = × z E r r and hence this vector function cannot represent an electrostatic field since all electrostatic fields have 0 = × E r r . (h) (True or False) The scalar function V(x,y,z) = xyz represents a possible electric potential for an electrostatic field with magnitude given by 2 2 2 2 2 2 ) , , ( y x z x z y z y x E + + = . (i) (True or False) The kinetic energy and the electric potential energy are always positive. (j) (True or False) In static equilibrium the electric field is always zero inside and on the surface of a conductor.

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PHY2061 R. D. Field Exam 1 Solutions Page 2 of 10 February 12, 2002 Problem 2 (15 points): Four identical point charges +Q are located at the corners of a square with sides of length L that lies in the xy-plane with a °2Q point charge at its center and with its center at the origin as shown in the Figure . Part A (3 points): What is the electric field vector, ) ( z E r , at a point P on the z-axis a distance z from the origin? ( Express your answer in terms of K, Q, L, and z and use vector notation ) Answer: z z L z z KQ E ² 2 ) 2 / ( 4 2 2 / 3 2 2 + = r Solution: The electric field at the point P is the superposition of the electric fields from each of the five charges as follows: z z L z z KQ z z KQ z r KQ E ² 2 ) 2 / ( 4 ² 2 ² cos 4 2 2 / 3 2 2 2 2 + = = θ r , where I used cos θ = z/r and 2 / 2 2 L z r + = . Part B (3 points): Which of the following gives the z-component of the electric field on the z-axis a distance z = L from the origin? ( circle one answer and show your work ) (a) 2.18 KQ/L 2 (b) 4.0 KQ/L 2 (c) -1.43 KQ/L 2 (d) 2.0 KQ/L 2 (e) -1.73 KQ/L 2 (f) 0.18 KQ/L 2 (g) 5.66 KQ/L 2 (h) none Solution: From Part A we have 2 2 / 3 2 2 2 / 3 2 2 18 . 0 2 ) 2 / 3 ( 4 2 ) 2 / ( 4 L KQ L KQ z L z z KQ E L z z = → + = = , Part C (3 points): What is the magnitude of the electric field on the z-axis when z becomes very large compared to the length, L , of the sides of the square? ( Hint : take the limit of the electric field when z >> L ) Answer: 2KQ/z 2 Solution: From Part A we have 2 2 2 / 3 2 2 2 2 ) 2 / ( 4 z KQ z L z z KQ E L z
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2061x1_solutions_sp02 - PHY2061 R D Field PHY 2061 Exam 1...

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