sol-e1-sum10 - Solutions Exam 1 Phy2049 Summer 2010 1. Two...

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A C Solutions Exam 1 Phy2049 Summer 2010 1. Two charges, q 1 = (-1, 1) C and q 2 = (-4, 9) C, are placed along the x-axis a distance L apart with charge q 1 at the origin and q 2 at x=L (see figure). A third charge, q 3 = (+4/9, -9/16) C, is also placed along the x-axis such that there is no net Coulomb force on any of the charges. What is position of this charge along the x axis in units of L, i.e. what is x/L? Answer (1/3, ¼) Solution: The force on charge 1 consists of repulsion due to charge 2 and the force due to the unknown charge 3 in the middle. Charge 3 must be of opposite sign to cancel the force due to 2. g G ± ²³ ´ µ ³ · ¸ ¹ ³ ¸ º ¸ » ± 0 · º ± √¼ ³ ³ ¸ ½ The charges here are all magnitudes since their signs are already used in determining the directions of the forces. 2. Suppose we have an insulating spherical ball of uniform charge density ρ and radius R. At what radius or radii from the center of the sphere is the electric field strength reduced by a factor of (16, 9) from the electric field strength at the surface? Answer: (R/16 and 4R, R/9 and 3R) The electric field due to a uniform distribution of charges in a sphere shaped insulator is given by ¾ ± ² ¿ 3 À À Á Â ± ² ¿Â ¸ À Ã Â The electric field can be smaller at two locations, smaller than R where the field increases linearly and at a position larger than R where the electric field decreases with the square of the
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sol-e1-sum10 - Solutions Exam 1 Phy2049 Summer 2010 1. Two...

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