Question

2 point charges 5 microcoulomb and 6 microcoulomb kept at a distance 12 cm apart. then, calculate the work done when 6 microcoulomb is moved by 2 cm towards the charge 5 microcoulomb.

Answer 1

$$\begin{gathered} Workdone=force.displacementi.e. \\ W=F.dr.Given{Q}_1=5\times {10}^{-6}C,Q_2=6\times {10}^{-6}C,r_1=.12m,r_2=.1m. \\ CoulombianforceofrepulsionF=k\times \frac{Q_1{Q}_2}{r^2}.WhereK=9\times {10}^9\frac{N{m}^2}{C^2}. \\ ThereforeW=K\times Q_1{Q}_2{\int }_{.12}^{.1}\frac{dr}{r^2}orW=9\times {10}^9\times 5\times {10}^{-6}\times 6\times {10}^{-6}(\frac{-1}{r}{)}_{.12}^{.1} \\ OrW=27\times {10}^{-2}\left[-\frac{1}{.1}+\frac{1}{.12}\right]OrW=27\times {10}^{-2}\left[-10+\frac{100}{12}\right]OrW=27\times {10}^{-2}\times \left(\frac{-20}{12}\right). \\ OrW=.45J. \end{gathered}$$