Question

If the vertical deflection of the electron as it leaves the plates is 9.00 mm, how much has its kinetic energy increased due to the electric field?

Answer 1

`\Delta K=7.2*10^(-19)J`

Step-by-step explanation:

According to the work-energy theorem, the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle:

`W=\Delta K`

Work is defined as the product of the force acting on the particle, the displacement due to that force and the cosine of the angle between them:

`W=Fdcos\theta`

The electric force on the electron is given by:

`F=eE`

In this case
`\theta=0^\circ` since the electric force is negative, the displacement is in the same direction, that is, opposite to the direction of the electric field. Finally, we calculate how much has electron's kinetic energy increased:

`eEdcos\theta=\Delta K\\\Delta K=-1.6*10^(-19)C(500(N)/(C))(-9*10^(-3)m)cos(0^\circ)\\\Delta K=7.2*10^(-19)J`