Problem 21.74 Part A Two tiny spheres of mass 5.80 mg carry charges of equal mag

Question

Problem 21.74 Part A Two tiny spheres of mass 5.80 mg carry charges of equal magnitude, 62.0 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 E that is directed to the left is turned on, the spheres hang at rest with the angle between the strings equal to 58.0° (Figure 1) Which ball (the one on the right or the one on the left) has positive charge? the one on the right the 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. Figure 1 of 1 ? 3.87 10 Submit My Answers Give Up Incorrect; Try Again; 9 attempts remaining vide Feedbac

Explanation / Answer

Look at the positive sphere. There are three forces: gravity down, the attraction to the negative charge horizontal to the right and the E field horizontal to the left.
We know that the sum of the horizontal forces Fx divided by the vertical force (mass*g) = tan25
We know the distance between the spheres = 2*0.53sin29 = 0.514 m
[62e-9*E - k*(62e-9)²/0.514²]/5.8e-6*9.8 = tan29
[62e-9*E - k*(62e-9)²/0.514²] = 5.8e-6*9.8* tan29
[62e-9*E = k*(62e-9)²/0.514²] + 5.8e-6*9.8* tan29
E = [k*(62e-9)²/0.514²] + 5.8e-6*9.8* tan29]/62e-9 = 2620.2 N/C

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