Speed of an Electron in an Electric Field (EC) Constants I Periodic Table Part A

Question

Speed of an Electron in an Electric Field (EC) Constants I Periodic Table Part A Two stationary positive point charges, charge 1 of magnitude 3.10 nC and charge 2 of magnitude 1.65 nC , are separated by a distance of 55.0 cm . An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges What is the speed Vinal of the electron when it is 10.0 cm from charge 1? Express your answer in meters per second. View Available Hint(s) Vfinal m/s Submit

Explanation / Answer

Solution) Charge q1=3.1nc=3.1×10^(-9)c

Charge q2=1.65nc=1.65×10^(-9)c

Radius R=55cm =0.55m

R1=R2=0.55/2=0.275m

Initial potential energy U1=kq1/R1 + kq2/R2

U1=(9×10^(9))×3.1×10^(-9)/(0.275)+(9×10^(9)×1.65×10^(-9)/0.275)

U1=155.45 J/C

Final potential energy U2 at R=10 cm

R=0.1m

U2=(9×10^(9)×3.1×10^(-9)/0.1 +(9×10^(9)×1.65×10^(-9)/(0.55-0.1)

U2=312 J/C

U2-U1=312-155.45

U2-U1=156.55e (e =1.6×10^(-19))

KE = U2-U1 ( change in potential energy)

(1/2)mv^2=156.55×1.6×10^(-19)

v^2=(156.55×2×1.6×10^(-19))/(9.1×10^(-31))

v=7.41×10^(6) m/s

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