Two tiny spheres of mass 8 80 mg carry charges of equal magnitude. 82 0 nC. but
ID: 1492203 • Letter: T
Question
Two tiny spheres of mass 8 80 mg carry charges of equal magnitude. 82 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 loft is turned on. the spheres hang at test with the Angle theta between the strings equal to 58 0degree. Which ball(the one on the right or the one on the left) has positive charge? What is the magnitude E of the field? Express your answer with the appropriate units.Explanation / Answer
R= horizontal distance betwen balls= sin ( 58/2) = R/2/ L
0.485 = ( R/2)/ 0.530
R = 0.485( 2)( 0.530) = 0.512 mapprx
Let's nalyze the forces applicable on a right ball,
along vertical axis,
FTcos ( 58/2) - mg = 0 ( where FT is the tension in the string)
FT = (8.80 x 10^-3)(9.8)/ 0.874 = 0.098 N apprx
along horizontal axis
FE- FQ- FTsin ( 58/2) = 0 ( where FE = force due to electric field towards + x axis and Fq is the between oppositely charged ball directed along - x axis)
82 x 10^-9 (E) - K( -82 )(+82)( 10^-18)/ (0.512 )^2 - 0.098( 0.484)= 0
82 x 10^-9 (E) + 2.3 ( 10^-4) - 0.047 =0
82 x 10^-9E = 0.0677
E = 5.7 x 10^5 N/c apprx
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