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