# 2-3 - Create assignment 00224 Homework 3 Feb 05 at 9:08 am...

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Create assignment, 00224, Homework 3, Feb 05 at 9:08 am 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Charge on Third Particle 23:05, trigonometry, numeric, > 1 min, wording-variable. 001 A particle with charge - 9 μ C is located on the x -axis at the point - 10 cm , and a sec- ond particle with charge 5 μ C is placed on the x -axis at 4 cm . The Coulomb constant is 8 . 9875 × 10 9 N · m 2 / C 2 . 2 4 6 8 10 - 2 - 4 - 6 - 8 - 10 - 9 μ C 5 μ C 2 μ C x (cm) What is the magnitude of the total elec- trostatic force on a third particle with charge 2 μ C placed on the x -axis at 2 cm ? Correct answer: 235 . 922 N. Explanation: Let : q 1 = - 9 μ C = - 9 × 10 - 6 C , q 2 = 5 μ C = 5 × 10 - 6 C , q 3 = 2 μ C = 2 × 10 - 6 C , x 1 = - 10 cm = - 0 . 1 m , x 2 = 4 cm = 0 . 04 m , and x 3 = 2 cm = 0 . 02 m . Coulomb’s law (in vector form) for the elec- tric force exerted by a charge q 1 on a second charge q 3 , written ~ F 13 is ~ F 13 = k e q 1 q 3 r 2 ˆ r 13 , where ˆ r 13 is a unit vector directed from q 1 to q 3 ; i.e. , ~r 13 = ~r 3 - ~r 1 . x 13 = x 3 - x 1 = (2 cm) - ( - 10 cm) = 0 . 12 m x 23 = x 3 - x 2 = (2 cm) - (4 cm) = - 0 . 02 m ˆ x 13 = x 3 - x 1 p ( x 3 - x 1 ) 2 = +ˆ ı ˆ x 23 = x 3 - x 2 p ( x 3 - x 2 ) 2 = - ˆ ı Since the forces are collinear, the force on the third particle is the algebraic sum of the forces between the first and third and the second and third particles. ~ F = ~ F 13 + ~ F 23 = k e q 1 r 2 13 ˆ r 13 + q 2 r 2 23 ˆ r 23 q 3 = 8 . 9875 × 10 9 N · m 2 / C 2 × ( - 9 × 10 - 6 C) (0 . 12 m) 2 (+ˆ ı ) + (5 × 10 - 6 C) ( - 0 . 02 m) 2 ( - ˆ ı ) × (2 × 10 - 6 C) = ( - 11 . 2344 N) + ( - 224 . 688 N) = - 235 . 922 N k ~ F k = 235 . 922 N . keywords: Magnitude of Force 23:05, highSchool, numeric, > 1 min, normal. 002 There are two identical small metal spheres with charges 33 μ C and - 26 . 4 μ C. The dis- tance between them is 5 cm. The spheres are placed in contact then set at their orig- inal distance. The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 .

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