An Empire starship fires a beam of electrons at Skywalker’s ship. Each electron has an initial kinetic energy of 1.6×10^{−17} J. The Skywalker’s ship has been fitted out with the electrostatic shield technology for defense against electron beam weapons. The electric field of the shield points directly inward. If the electrons stop after travelling 83 m, what is the size of the electric field generated by the ship’s shield? Please ignore relativistic effects.

###### Solution.

The electron stops after travelling 83 m. It is meant that electron has lost all of its kinetic energy. The kinetic energy spent on work done against the electric force. We can write it as

E_{k} = W

The work is defined as:

W = F*x*cosθ

where is the displacement the object was moved, F is the force by which it was moved and θ is the angle between force and the displacement.

θ = 0, thus

W = F*x.

Also, the electric field E is given by

E = F/q or F = q*E

where q, in our case, is the charge on an electron 1.60×10^{−19} C.

Thus,

E_{k} = W = F*x = q*E*x

and finally,

E = E_{k} / (q*x) = 1.6×10^{−17} / (1.60×10^{−19} * 83) = 1.2 V/m.