2061x1_solutions_fa03

2061x1_solutions_fa03 - PHY2061 R. D. Field PHY 2061 Exam 1...

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PHY2061 R. D. Field Exam 1 Solutions Page 1 of 9 September 30, 2003 PHY 2061 Exam 1 Solutions Problem 1 (10 points): Circle true or false for following (1 point each). (a) (True or False) The electrostatic force is much weaker than gravity. (b) (True or False) Electric field lines 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) Negatively charged particles move from low to high potential. (e) (True or False) Electric field vectors are tangent to lines of constant potential. (f) (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 + + = . (g) (True or False) The scalar function V(x,y,z) = x 2 -y 2 -z 2 represents an electric potential for an electrostatic field with magnitude given by 2 2 2 2 ) , , ( z y x z y x E + + = and 0 = × E r r . (h) (True or False) The line integral of the electrostatic field around any closed loop is always zero. (i) (True or False) The divergence of the electric field is always zero. (j) (True or False) The electric field has energy and mass.
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PHY2061 R. D. Field Exam 1 Solutions Page 2 of 9 September 30, 2003 Problem 2 (18 points): An electric dipole is placed on the x-axis with +Q at x = d/2 and -Q at x = -d/2 , 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 in the region x > d/2 ? ( Express your answer in terms of K, Q, d, and x . and take V = 0 at infinity ) Answer: 2 2 ) 2 / ( ) ( d x KQd x V = Solution: The electric potential at the point A on the x-axis is the superposition of the electric potentials from each of the two charges as follows: 2 2 2 1 ) 2 / ( ) 2 / )( 2 / ( ) 2 / ( ) 2 / ( ) 2 / ( ) 2 / ( d x KQd d x d x d x d x KQ d x KQ d x KQ V V V = + + = + = + = 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) 1.33 KQ/d (f) -1.33KQ/d (g) zero (h) none Solution: From Part A we see that d KQ d KQ d d KQd d x V 33 . 1 3 4 ) 2 / ( ) ( 2 2 = = = Part C (3 points): Which of the following gives the value of the electric potential on the y-axis a point B a distance y = 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) 1.33 KQ/d (f) -1.33KQ/d (g) zero (h) none Solution: The electric potential at any point B on the y-axis is the superposition of the electric potentials from each of the two charges as follows: 0 2 1 = = + = r KQ r KQ V V V Part D (3 points): What is the x-component of electric field, E x (x) , at a point on the x-axis a distance x from the origin in the region x > d/2 ? ( Express your answer in terms of K, Q, d, and x .) Answer: 2 2 2 ) ) 2 / ( ( 2 ) ( d x KQxd x E x = Solution: The electric field is calculated from the electric potential as follows: +Q d -Q x-axis A y-axis B
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PHY2061 R. D. Field Exam 1 Solutions Page 3 of 9 September 30, 2003 2 2 2 ) ) 2 / ( ( 2 ) ( d x KQxd dx dV x E x = = , where V(x) was calculated in Part A.
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2061x1_solutions_fa03 - PHY2061 R. D. Field PHY 2061 Exam 1...

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