2061x1_solutions_fa02

2061x1_solutions_fa02 - PHY2061 R. D. Field PHY 2061 Exam 1...

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PHY2061 R. D. Field Exam 1 Solutions Page 1 of 8 October 1, 2002 PHY 2061 Exam 1 Solutions Problem 1 (20 points): Circle true or false for following (2 points each). (a) (True or False) Unlike gravity the electrostatic force can be both attractive and repulsive. (b) (True or False) Electric field lines never cross. (c) (True or False) Positively charged particles move from low to high potential. (d) (True or False) In a region of space where the electric potential is constant there can be no charged particles. (e) (True or False) The vector function z x y y x z 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 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 scalar function V(x,y,z) = x 2 yz represents a possible electric electrostatic field in a vacuum. Note that 0 2 0 = V ε ρ and hence these is a non zero charge density which cannot be true in a vacuum. (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 October 1, 2002 Problem 2 (20 points): Three point charges are placed on the y-axis with -Q at y = d/2, -Q at y = -d/2 , and +2Q at y = 0 , as shown in the Figure . Part A (3 points): What is the electric potential, V(x) , on the x-axis a distance x from the origin? ( Express your answer in terms of K, Q, d, and x . and take V = 0 at infinity ) Answer: 2 2 ) 2 / ( 2 2 ) ( d x KQ x KQ x V + = Solution: The electric potential at the point x on the x-axis is the superposition of the electric potentials from each of the three charges as follows: 2 2 ) 2 / ( 2 2 2 ) ( d x KQ x KQ r KQ r KQ x KQ x V + = = , where I used and 2 2 ) 2 / ( d x r + = . Part B (3 points): Which of the following gives the value of the electric potential on the x-axis a point A a distance x = d from the origin? ( circle one answer and show your work, and take V = 0 at infinity ) (a) 0.67 KQ/d (b) 0.21 KQ/d (c) -0.67 KQ/d (d) -0.21 KQ/d (e) 1.5 KQ/d (f) KQ/d (g) zero (h) none Solution: From Part A the electric potential at the point A on the x-axis is given by: d KQ d KQ d d KQ d KQ d x V 21 . 0 5 2 1 2 ) 2 / ( 2 2 ) ( 2 2 = = + = = , Part C (3 points): What is the electric potential, V(y) , on the y-axis a distance y > d/2 from the origin? ( Express your answer in terms of K, Q, d, and y . and take V = 0 at infinity ) Answer: ) ) 2 / ( ( 2 ) ( 2 2 2 d y y KQd y V = Solution: The electric potential at the point y on the y-axis is the superposition of the electric potentials from each of the three charges as follows: ) ) 2 / ( ( 2 ) 2 / ( 2 2 ) 2 / ( ) 2 / ( 2 ) ( 2 2 2 2 2 d y y KQd d y KQy y KQ d y KQ d y KQ y KQ y V = = + = .
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2061x1_solutions_fa02 - PHY2061 R. D. Field PHY 2061 Exam 1...

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