Respuesta :
Answer: 1.85*10^-27 C/m^2
Explanation: In order to explain this problem, firstly we have to consider the kinematic equations given by:
xf=vo*t-(a*t^2)/2 and we considerer xo=0 and xf= 15 cm the distance that the electron moves before changes its direction of movenet due to the influence of the electric field from the negative charged plate.
and
vf=vo-a*t vf=0 when the electron starts to be repelled.
From these equations we have:
t=vo/a put it in the distante equation we have:
xf=vo*vo/a-(a/2)*(vo/a)^2 then xf=vo^2/a-(vo^2/2*a)= vo^2/(2*a)=
0.15 m=(8.3*10^6)^2/(2*a)
we have used that: vo=8300 Km/s= 8300 km/s*1000 m/km=8.3*10^6m/s
a= (8.3*10^6)^2/(2*0.15)=5.74*10^13 m/s^2
Secondly, we use the second Newton law:
F=m*a where the force from the electric field is given by:
Fe=σ/εo where σ is the surface charge density and the vaccum pernitivity is εo=8.85*10^-12 C^2/m^2*N
Finally, we have
Fe= σ/εo = m*a
σ= m*a *εo= 9.1 *10^-31* 5.74*10^13 *8.85*10^-12=1.85*10^-27 C^2/m^2
