1) what is the acceleration felt by a free electron in a metal if the magnitude

Question

1) what is the acceleration felt by a free electron in a metal if the magnitude of

the electric field is E?

2) suppose we start with an electron with zero initial velocity. Let be

the typical time it would take for our electron to hit an atom. We can use this as

an average time between collisions as the electron makes its way through the

material. What is the typical velocity of the electron when it hits an atom?

2

3) It turns out that the velocity you just calculated is not a bad estimate of the drift

velocity, vd. Now, as we saw, there is another way to write vd, namely

J = (ne)vd for electrons (remember J = i / A for uniform current density), where

n is the number of charge carriers (electrons) per unit volume. Solve this for |vd|

and equate with what you got in (2).

Explanation / Answer

apply ma = Eq

so accleration a = Eq/m

b. drift velocity Vd = -eET/me

where T is the time taken

e is charge

E is applied EF

me is mass of the eelctrcon

c. current I = dQ/dt

I = ne (AVd)

I = -neA * nET/me

= ne^2T AE/me

I = AE/rho

where rho = me/ne^2T

so I = AdV/(rho L)

R = rho L/A

so Vd = i/neA

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