Please help and do it step by step all parts of questions and use:
T = time(s)
I=current (amps)
Q=net charge on object (Coulombs)
N=no electrons (and write if added or removed from object and how)
E=elementary charge
Calculate the number of free electrons per metre length of wire if a current of 2.0A produces a drift velocity of 1.0 x 10^-3 ms-1.
As physics - bobpursley Tuesday, December 12, 2017 at 10:27am
current=driftevelocity*area*electrondensity
but number electrons per lenth=electron dinsity)*area
the equation i=anev
n=work out
i=2
a=???
v= 1.0 X 10^-3 ms-1
was what i thought at first but then 2 values were missing when only one should be then you said number "NUMBER electrons per lenth=electron dinsity)*area"
but i dont know the density of the electrons or the area pelase help
is there a way to work this out?
i cant find the numbers for the equation yo gave me
"NUMBER electrons per lenth=electron dinsity)*area"
an Ampere is a coulomb per sec
2 coulombs per sec
... 6.24E18 electrons per coulomb
drift velocity is ... 1.0E-3 m/s
so there are (2 * 6.24E18) free electrons in 1.0E-3 m of wire
To calculate the number of free electrons per meter length of wire, we need to find the electron density and the area of the wire.
Step 1: Find the electron density (n)
The equation i = anev relates the current (i) in the wire to the drift velocity (v), electron density (n), and the cross-sectional area (a) of the wire. Since we know the current and the drift velocity, we can rearrange the equation to solve for the electron density (n).
i = anev
Solving for n:
n = i / (ave)
Where:
i = 2.0 A (given in the question)
v = 1.0 x 10^-3 m/s (given in the question)
a = unknown (we need to find this)
Step 2: Find the cross-sectional area (a)
To find the area of the wire, we need to know the shape of the wire. Let's assume it is a cylindrical wire. The area of a circle is given by the formula:
A = πr^2
Where:
A = Area
π = pi (approximately 3.14159)
r = radius of the wire
If you have the radius of the wire, substitute it into the formula to get the area. If you have the diameter, you can convert it to radius by dividing it by 2.
Step 3: Calculate the number of electrons per meter length of wire
Now that we have the electron density (n) and the area (a), we can calculate the number of electrons per meter length of wire.
Number of electrons per meter length = (electron density) * (cross-sectional area)
Substitute the values of n and a into the equation to calculate the number of electrons per meter length.
Please note that the units used for the cross-sectional area and length should be consistent. If the cross-sectional area is given in square meters, then the length should also be in meters.
I hope this step-by-step explanation helps you in solving the problem. Let me know if you need any further assistance.