Question

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.28 m . If g =10 ms^-2,what is the charge on each ?
Answer 1.594x10^-8C

Answer 1

$$\begin{gathered} Weightofthesphere=10mg={10}^{-5}kg \\ ifthestringmakesanangle\theta withvertical \\ then\sin \theta =\frac{0.14}{0.5}=0.28 \\ \theta =16.26degree \\ nowT\cos (16.26)=mg \\ T=\frac{{10}^{-5}\times 10}{0.96}=1.041\times {10}^{-4} \\ andT\sin \theta =k\frac{q^2}{x^2} \\ {q}^2=\frac{1.041\times {10}^{-4}\times 0.28\times (0.28{)}^2}{8.99\times {10}^9}=.0025\times {10}^{-13} \\ q=1.59\times {10}^{-8}Cistheamountofchargeineachsphere \end{gathered}$$