2061x1_solutions_sp03

# 2061x1_solutions_sp03 - PHY2061 R D Field PHY 2061 Exam 1...

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PHY2061 R. D. Field Exam 1 Solutions Page 1 of 8 February 11, 2003 PHY 2061 Exam 1 Solutions Problem 1 (20 points): Circle true or false for following (2 points each). (a) (True or False) The electrostatic force is much weaker than gravity. (b) (True or False) Electric field lines do not touch because they repel each other. (c) (True or False) Positively charged particles move from low to high potential. (d) (True or False) Electric field vectors are tangent to lines of constant potential. (e) (True or False) The vector function z z y x x y z y x E ˆ ˆ ˆ ) , , ( + = r represents a possible electrostatic field with magnitude given by 2 2 2 ) , , ( z y x z y x E + + = . Note that 0 × E r r and hence this vector function can not represent an electrostatic field. (f) (True or False) The scalar function V(x,y,z) = x 2 +y 2 +z 2 represents a possible electric potential for an electrostatic field with magnitude given by 2 2 2 2 ) , , ( z y x z y x E + + = . (g) (True or False) The line integral of the electrostatic field around any closed loop is always zero. (h) (True or False) The net electric flux through a closed surface is always positive or zero. (i) (True or False) The divergence of the electric field is always zero. (j) (True or False) The electric field has energy but no mass.

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PHY2061 R. D. Field Exam 1 Solutions Page 2 of 8 February 11, 2003 Problem 2 (20 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 +4Q point charge at its center and with its center at the origin as shown in the Figure . The total charge of the system is zero. Part A (4 points): What is the electric potential, V(z) , on the z-axis a distance z from the origin? ( take V = 0 at infinity and express your answer in terms of K, Q, L, and z ) Answer: + = 2 / 1 1 4 ) ( 2 2 L z z KQ z V Solution: The electric potential at the point P is the superposition of the potentials from each of the five charges as follows: + = = 2 / 1 1 4 4 4 ) ( 2 2 L z z KQ r KQ z KQ z V , where I used 2 2 ) 2 / ( L z r + = . Part B (4 points): Which of the following gives the electric potential, V , on the z-axis a distance z = L from the origin ( circle one answer and show your work and take V = 0 at infinity ) (a) 2.2 KQ/L (b) 4.0 KQ/L (c) 5.7 KQ/L (d) 0.82 KQ/L (e) 4.7 KQ/L (f) 0.18 KQ/L (g) 5.4 KQ/L (h) none Solution: From part A we see that L KQ L KQ L z z KQ z V L z 734 . 0 2 / 3 1 1 4 2 / 1 1 4 ) ( 2 2 → + = = . Part C (4 points): What is the z-component of the electric field, E z (z) , on the z-axis a distance z from the origin? ( express your answer in terms of K, Q, L, and z ) Answer: + = 2 / 3 2 2 2 ) 2 / ( 1 4 L z z z KQ E z Solution: The electric field is calculated from the electric potential as follows: + = = 2 / 3 2 2 2 ) 2 / ( 1 4 L z z z KQ z V E z .
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2061x1_solutions_sp03 - PHY2061 R D Field PHY 2061 Exam 1...

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