Mastering Physics: Homework M-Google Chrome Secure https:// masteringphysics.com
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Mastering Physics: Homework M-Google Chrome Secure https:// masteringphysics.com session Physics 158 Homework 4 Problem 21.74 Problem 21.74 Two tiny spheres of mass 6.80 mg carry charges of equal magnitude, 77.0 nC but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field Ethat is directed to the left is tumed on, the spheres hang at rest with the angle between the strings equal to 58.0 (Eigure 1) Figure assignmentProblemID 76225567 Part A Which ball (the one on the right or the one on the left) has positive charge? the one on the right he one on the left Submit My Answers Give Up Correct Part B What is the magnitude E of the field? Express your answer with the appropriate units. E+ Value Units Submit ML Answers Give Up Help Close Resources T x previous 5 of 6 l nextExplanation / Answer
Forces acting on the positive charge is
vertically downward weight (m*g)= 6.8*10^-6*9.8= 6.664*10^-5 N
Horizontal force towards right is Electorstatic force between two charges Fe = k*q^2/r^2
r is the distance between them = 2*L*sin(58/2) = 2*0.53*sin(58/2) = 0.513 m
then Fe = k*q^2/r^2 = 9*10^9*(77*10^-9)^2/(0.513^2)
Fe = 2.02*10^-4 N
Electric force by field is F = q*E = 77*10^-9*E towards left
Net horizontal force is Fh = 2.02*10^-4 - (77*10^-9*E)
tan(25) = Fh/w = (2.02*10^-4 - (77*10^-9*E))/(6.664*10^-5)
0.466 = (2.02*10^-4 - (77*10^-9*E))/(6.664*10^-5)
E = 2.22*10^3 N/C = 2.22 kN/C