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2061x3_solutions_fa02

# 2061x3_solutions_fa02 - PHY2061 R D Field PHY 2061 Final...

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PHY2061 R. D. Field Final Exam Solutions Page 1 of 8 December 10, 2002 PHY 2061 Final Exam Solutions Problem 1 (20 points): Circle true or false for following (2 points each). (a) (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 ˆ 2 = × y E r r and hence this vector function cannot represent an electrostatic field since all electrostatic fields have 0 = × E r r . (b) (True or False) The vector function z x y y x z z y x B ˆ ˆ ˆ ) , , ( + = r represents a possible magnetic field with magnitude given by 2 2 2 ) , , ( z y x z y x B + + = . Note that 0 1 = B r r and hence this vector function cannot represent a magnetic field since all magnetic fields have 0 = B r r . (c) (True or False) The electric field is zero on the surface of all conductors in static equilibrium. (d) (True or False) It is possible to construct both electric and magnetic dipole field configurations, but it is not possible to construct an electric monopole field. (e) (True or False) Lines of constant electric potential are always perpendicular to electric field lines. (f) (True or False) In relativity, energy and momentum are conserved, but mass and electric charge are not. (g) (True or False) When light moves from one medium to another both its speed and wavelength change, but its frequency remains the same. (h) (True or False) It is possible for a proton to travel through water faster than light travels through water. (i) (True or False) The real image created by a concave mirror is always inverted. (j) (True or False) Convex mirrors can produce both real and virtual images.

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PHY2061 R. D. Field Final Exam Solutions Page 2 of 8 December 10, 2002 Problem 2 (20 points): Consider the situation illustrated in the figure . A uniform external electric field points in the z-direction ( out of the paper ) with a value given by E z (t) =E 0 + at 2 , where E 0 = -808 V/m and a = 200 V/(m s 2 ) . Also, a uniform external magnetic field points in the z-direction with a value given by B z (t) = B 0 + bt 2 , where B 0 = 8 T and b = -2 T/s 2 . Both external fields are confined to a circular region with a radius R , where R = 2 meters . (c 2 = 1/( µ 0 ε 0 ), c = 3 x 10 8 m/s, µ 0 = 4 π x 10 −7 Tm/A) Part A (5 points): What is the magnitude of the induced electric field ( in V/m ) at the point P on the circumference of the circle of raduis R at the time t = 2 seconds ? Answer: 8 Solution: We know from Faraday's Law that Φ = dt d l d E B r r . If I choose my orientation to by counter-clockwise then Φ B = B π R 2 and bt R dt dB R R RE 2 ) ( 2 2 2 π π π = = , and solving for the induced electric field E gives m V s s T m Rbt R E / 8 ) 2 )( / 2 )( 2 ( ) ( 2 = = = . Since E is positive the field lines point in the direction of my orientation ( counter- clockwise ). Part B (3 points): Which of the following gives the direction of the induced electric field lines at the point P on the circumference of the circle of raduis R at the time t = 2 seconds ? ( circle one ) (a) counter-clockwise (b) clockwise Part C (4 points): What is the magnitude of the net electric field ( in V/m
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2061x3_solutions_fa02 - PHY2061 R D Field PHY 2061 Final...

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