The current
I=80A, and the length of the conductor
L=10m.
Expression for Current:
Current can be written as
I=neAVd, where
n is the number of electrons per unit volume,
e is the charge of an electron,
A is the cross-sectional area, and
Vd is the drift velocity of electrons.
Total Number of Electrons:
Let
N be the total number of free electrons in the length
L of the conductor.
N=nAL.
Total Momentum:
The total momentum of all free electrons is
P‌total ‌=N(meVd), where
me is the mass of an electron.
Substitute
N :
So,
P‌total ‌=(nAL)(meVd).
Rewrite with Current Expression:
Since
I=neAVd, we can replace
nAVd with
‌.
Therefore,
P‌total ‌=(I∕e)Lme.
Simplified Formula:
So,
P‌total ‌=I‌.
Plug in the Values:
P‌total ‌=80×‌| 10×9.1×10−31 |
| 1.6×10−19 |
First, multiply
80×10=800.
Now
800×9.1=7280.
So, numerator is
7280×10−31 and denominator is
1.6×10−19.
Divide 7280 by 1.6 to get 4550 .
Power of ten:
10−31∕10−19=10−12Final Answer:
P‌total ‌=4550×10−12N−s=4.55×10−9N−s=455×10−11N−s