The electrons in a particle beam each have a kinetic energy K. What is the magnitude of the electric field that will stop these electrons in a distance d?

Electric field magnitude

E = K/qd

Where

K = kinetic energy of electron

d = electron distance

q = charge

Explanation:

Given the relationship between workdone and energy

Work-energy theorem:

Net workdone = Energy change

W = ∆E

In this case

W = ∆K. E

And,

∆K. E = K (final) - K (initial)

To stop the kinetic energy | K (final) = 0

K (initial) = K (given)

∆K. E = 0 - K = - K

Let the electric force on the electron has magnitude F.

And

W = - Fd = ∆K. E = - K

-Fd = - K

F = K/d ... 1

The magnitude of the electric field E that can stop these electron in a distance d:

E = F/q ... 2

Where q is the charge on electron.

substituting equation 1 to 2

E = (K/d) / q = K/qd

E = K/qd