Two small plastic spheres are given positive electricalcharges. When they are 17

Question

Two small plastic spheres are given positive electricalcharges. When they are 17.0 cm apart, the repulsive forcebetween them has magnitude 0.300 N. a) What is the charge on each sphere if the two charges areequal?      Q=       C b)What is the charge on each sphere if one sphere has fourtimes the charge of the other?          Q1Q2=        C Two small plastic spheres are given positive electricalcharges. When they are 17.0 cm apart, the repulsive forcebetween them has magnitude 0.300 N. a) What is the charge on each sphere if the two charges areequal?      Q=       C b)What is the charge on each sphere if one sphere has fourtimes the charge of the other?          Q1Q2=        C

Explanation / Answer

(a) Let q be the charge of the two charged spheres. The seperation (d) between them = 17.0 cm = 0.170 m Force (F) of repulsion between them = 0.300 N Then from the Coulomb's law                  F = (9.0*109N.m2/C2)(q2/ d2)            0.300N =(9.0*109N.m2/C2)(q2) /(0.170m)2                 q2 = (0.300 N)(0.170m)2/(9.0*109N.m2/C2)                  q = 0.98*10-6C                     = 0.98 C (b) Now given that q1 = q and q2 = 4q Then F =(9.0*109N.m2/C2)(4q2 /d2)         0.300N =4(9.0*109N.m2/C2)(q2 /d2)       0.300 N =4(9.0*109N.m2/C2)(q2) /(0.170m)2          q2 = (0.300 N)(0.170m)2/4(9.0*109N.m2/C2)            q =0.49 C Now q1 = 0.49C          q2 = 4q= 4(0.49C) = 1.96C

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