A body having specific charge 8μC/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ____ s.
Answer: 1
Solution
The specific charge is mq=8μC/g=10−38×10−6=8×10−3C/kg, so the field gives the body an acceleration
a=mqE=8×10−3×100=0.8m/s2
Starting from rest it covers d=0.1 m in
t=a2d=0.80.2=0.5s
The collision is perfectly elastic, so the body leaves the wall with the speed it arrived with, while the field still points towards the wall and decelerates it at the same rate; it therefore returns to its starting point, momentarily at rest, after a further 0.5 s. The motion repeats from there, so the time period is 2×0.5=1 s.
