A dipole consisting of a protons and an electron held a distance d apart is aligned along a z axis. A second proton is then placed at the midpoint of the line joining the electron and proton of the dipole. What is the ratio of the electric field magnitude at (0, 0, 10d) to the electric field magnitude at (0, 0, 20d)?
suppose the proton is at (0,0,-d/2) and
electron is at (0,0,d/2)
and second proton is at (0,0,0)
electric field at (0,0,10d) is E = E1+E2+E3
E1 is the field due to first proton = ke*q/r^2 = (ke*q/(10.5d)^2) = 0.0091ke*q/d^2
E2 is the Field due to electron = -ke*q/(9.5d)^2 = -0.011*ke*q/d^2
E3 is the Field due to second proton = ke*q/(10d)^2 = 0.01*ke*q/d^2
E = E1+E2+E3 = (0.0091-0.011+0.01)*(ke*q/d^2) = 0.0081*(ke*q/d^2)
field at (0,0,20d) is E = E1+E2+E3
E = (ke*q/d^2)((1/20.5^2)-(1/19.5^2)+(1/20^2)) = 0.00224*ke*q/d^2
then required ratio is 0.0081/0.00224 = 3.62
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