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Unformatted text preview: PHY2061 R. D. Field Final Exam Solutions Page 1 of 10 April 23, 2002 PHY 2061 Final Exam Solutions Problem 1 (10 points): Circle true or false for following (1 point each). (a) (True or False) The vector function z x y y x z z y x E & & & ) , , ( + + = r represents a possible electrostatic field with magnitude given by 2 2 2 ) , , ( z y x z y x E + + = . Note that = × ∇ E r r and hence this vector function can represent an electrostatic field. (b) (True or False) The vector function z x y y x z z y x B & & & ) , , ( + + = r represents a possible magnetic field with magnitude given by 2 2 2 ) , , ( z y x z y x B + + = . Note that 1 ≠ = ⋅ ∇ B r r and hence this vector function cannot represent a magnetic field since all magnetic fields have = ⋅ ∇ B r r . (c) (True or False) In a region of space where the electric potential is constant there can be no charged particles. Note that for V = C, = ∇ − = V E r r and hence = ⋅ ∇ = E r r ε ρ . (d) (True or False) The net magnetic flux through a closed surface is always zero. (e) (True or False) It is possible to construct magnetic monopole and magnetic dipole field configurations. (f) (True or False) In relativity, energy, momentum, and mass are conserved. Note that mass is not conserved. (g) (True or False) When light moves from one medium to another both its speed and wavelength change. (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 virtual image created by a concave mirror is always enlarged and upright. (j) (True or False) For convex mirrors, the distance between the image and the mirror is always shorter than the distance between the object that created the image and the mirror. PHY2061 R. D. Field Final Exam Solutions Page 2 of 10 April 23, 2002 Problem 2 (15 points): Two point charges +Q and two point charges Q are placed at the corners of a square with sides of length L as shown in the Figure. (Note: K = 1/(4 πε )). Part A (3 points): Which of the following gives the magnitude of the electric field at the point P 1 at the center of the square? ( circle one answer and show your work ) (a) 15.8 KQ/L 2 (b) 5.7 KQ/L 2 (c) 8 KQ/L 2 (d) 2.8 KQ/L 2 (e) 4 KQ/L 2 (f) 11.3 KQ/L 2 (g) zero (h) none Solution: The electric field at P 1 is the vector superposition of the electric fields of the four charges as follows: x L KQ x L KQ x L KQ x r KQ E & 66 . 5 & 2 8 & 2 1 2 / 4 & cos 4 2 2 2 2 = = = = θ r , where 2 / 2 / 2 L L r = = . Part B (4 points): Which of the following gives the electric potential difference, ∆ V = V 2V 1 between the point P 2 on the side of the square at the midpoint of the line between the two positive charges and the point P 1 at the center of the square? ( circle one answer and show your work ) (a) 15.8 KQ/L (b) 15.8 KQ/L (c) 5.8 KQ/L (d) 2.2 KQ/L (e) 1.9 KQ/L (f) 1.9 KQ/L (g) zero (h) none Solution: The electric potential at the point P 2 is given by L KQ L KQ r KQ L KQ...
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 Spring '08
 FRY
 Physics, Electric Potential, Magnetic Field, Total internal reflection

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