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midterm2 sol - Midterm 2 Physics 1B Name ID number...

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Midterm 2 Physics 1B —————————————————— Name: —————————————————— ID number: —————————————————— Lecture (1 or 2): Section (A-F): —————————————————— 1
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VARIANT-I 1. Four point charges form a square, as shown in the figure. The charges are q 1 = Q , q 2 = q 3 = q , and q 4 = - 2 Q . What is the ratio q/Q if the net electrostatic force on particle 1 is zero? Solution. The net force is equal to the sum of Coulomb forces vector F 2 , vector F 3 , vector F 4 due to the charges q 2 , q 3 , q 4 , respectively: vector F = vector F 2 + vector F 3 + vector F 4 = 0 In projection to the horizontal axis, this gives kQ ( - 2 Q ) ( 2 a ) 2 cos π 4 + kQq a 2 = 0 q Q = 2 2 For this ratio of charges, the projection of the forces to the vertical axis vanishes as well. ——————————————————- VARIANT-II 1. Four point charges form a square, as shown in the figure. The charges are q 1 = Q , q 2 = q 3 = q , and q 4 = - 8 Q . What is the ratio q/Q if the net electrostatic force on particle 1 is zero? Solution. The net force is equal to the sum of Coulomb forces vector F 2 , vector F 3 , vector F 4 due to the charges q 2 , q 3 , q 4 , respectively: vector F = vector F 2 + vector F 3 + vector F 4 = 0 In projection to the horizontal axis, this gives kQ ( - 8 Q ) ( 2 a ) 2 cos π 4 + kQq a 2 = 0 q Q = 2 2 For this ratio of charges, the projection of the forces to the vertical axis vanishes as well.
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