Two point charges $$q1$$ and $$q2$$ are fixed at a distance $$3.0$$ cm as shown in the figure. A dust particle with mass $$m=5.0$$×$$10$$−$$9$$ kg and charge $$q0=2.0nC$$ starts from rest at point 'a' and moves in a straight line to point ‘b’. What is its speed v at point b (in$$ $$m/s) ? (round$$ off to nearest $$integer)

Question

Two point charges $$q1$$ and $$q2$$ are fixed at a distance $$3.0$$ cm as shown in the figure. A dust particle with mass $$m=5.0$$×$$10$$−$$9$$ kg and charge $$q0=2.0nC$$ starts from rest at point 'a' and moves in a straight line to point ‘b’. What is its speed v at point b (in$$ $$m/s) ? (round$$ off to nearest $$integer)

Infinity Learn · Accepted Answer

Applying conservation of mechanical energy Δ$$K+$$Δ$$U=0or$$ Kf−$$Ki+Uf$$−$$Ui=0Here$$, $$Ki=0$$ and $$Kf=12mv2$$ and $$Ui=q0Vi$$ and $$Uf=q0VfHence$$, Kf−$$Ki+q0Vf$$−$$Vi=012mv2$$−$$0+q0Vf$$−$$q0Vi=0And$$ solving for v, we find, $$v=2q0Vi$$−Vfm            …(i) Electric potential at 'a':$$Vi=14$$πε$$0q1r1a+14$$πε$$0q2r2aVi=9.0$$×$$109$$×$$3.0$$×$$10$$−$$90.010+$$−$$3.0$$×$$10$$−$$90.020=1350$$ V      …(ii)Electric$$ potential at  'b′: $$Vf=14$$πε$$0q1r1b+14$$πε$$0q2r2bVf=9.0$$×$$109$$×$$3.0$$×$$10$$−$$90.020+$$−$$3.0$$×$$10$$−$$90.010=$$−$$1350$$ V       …$$(iii)From$$ $$(i), (ii) and (iii) we get $$v=22.0$$×$$10$$−$$9$$[(1350)−$$($$−$$1350)$$]$$5.0$$×$$10$$−$$9=46$$ $$m/srounding$$ off to nearest integer

Two point charges q1 and q2 are fixed at a distance 3.0 cm as shown in the figure. A dust particle with mass m=5.0×10−9 kg and charge q0=2.0nC starts from rest at point 'a' and moves in a straight line to point ‘b’. What is its speed v at point b (in m/s) ? (round off to nearest integer)

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!