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  4. Two identical charges repel each other with a force equal to 10 mgwt when they are 0.6 m apart in air.( g = 10 ms-2 ) The value of each charge is

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Q. Two identical charges repel each other with a force equal to $10\, mgwt$ when they are $0.6\, m$ apart in air.$( g = 10 ms^{-2} )$ The value of each charge is

KCETKCET 2007Electric Charges and Fields

Solution:

$ F=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q^{2}}{r^{2}} \\ 10 \times 10^{-3} \times 10 =\frac{9 \times 10^{9} Q^{2}}{(0.6)^{2}} \\ Q^{2} =\frac{(0.6)^{2} \times 10^{-1}}{9 \times 10^{9}} \\ =\frac{(0.6)^{2}}{(3)^{2}} \times 10^{-10} \\ Q =\frac{0.6}{3} \times 10^{-5} \\ =0.2 \times 10^{-5} \\ =2 \times 10^{-6} \\ =2 \mu C \\ $