The drift velocity of electrons through a point in a wire of radius 2.5 x 10-3 m is
1'5 x 10-s m/s' calculate the number of electrons passing the point for an electric
current of 10'4 through the wire. (Hint: Assume the wire has a circular cross-section)
To calculate the number of electrons passing through a point in a wire, we need to use the formula:
n = I / (A * q * v)
Where:
n - number of electrons
I - electric current (10^4 A)
A - cross-sectional area of the wire (πr^2)
q - charge of an electron (-1.6 x 10^-19 C)
v - drift velocity of electrons (1.5 x 10^-5 m/s)
First, we need to calculate the cross-sectional area of the wire using the given radius:
r = 2.5 x 10^-3 m
A = πr^2
A = π * (2.5 x 10^-3)^2
A = π * 6.25 x 10^-6
A = 1.96 x 10^-5 m^2
Now, let's substitute the values into the formula:
n = (10^4 A) / (1.96 x 10^-5 m^2 * -1.6 x 10^-19 C * 1.5 x 10^-5 m/s)
Calculating this expression gives us:
n ≈ 6.41 x 10^22
Therefore, approximately 6.41 x 10^22 electrons pass through the point in the wire for an electric current of 10^4 A.
To calculate the number of electrons passing through a point in a wire, we need to determine the total charge passing through that point and then divide it by the charge of a single electron.
Let's start by finding the total charge passing through the wire. The electric current (I) is given as 10.4 A (amperes). Electric current is defined as the rate of flow of charge, so it is equal to the charge passing through a point in a given time.
The charge passing through the wire in a time interval Δt can be calculated using the formula:
Q = I * Δt
Since we want to find the number of electrons passing through the point, we need to find the charge in terms of elementary charges (e), the charge of a single electron.
The charge of a single electron (e) is approximately 1.6 * 10^(-19) C (coulombs). Therefore, the total charge (Q) passing through the wire in terms of elementary charges (Ne) is given by:
Ne = Q / e
We are given the drift velocity (v) of electrons, which is 1.5 * 10^(-5) m/s (meters per second). The drift velocity is the average velocity of the electrons moving through the wire.
The formula for drift velocity (v) is given as:
v = I / (n * A * e)
Where:
- I is the electric current,
- n is the number density of electrons per unit volume,
- A is the cross-sectional area of the wire, and
- e is the charge of a single electron.
We are also given the radius (r) of the wire, which is 2.5 * 10^(-3) m. The cross-sectional area (A) of the wire can be calculated using the formula:
A = π * r^2
Now, let's calculate the cross-sectional area (A) of the wire:
A = π * (2.5 * 10^(-3))^2
= π * 6.25 * 10^(-6)
≈ 1.963495408 * 10^(-5) m^2
To find the number density of electrons (n), we need to know the material of the wire and its properties. Without this information, we won't be able to calculate the exact value of n. So, let's assume a value for n for the purpose of this exercise. Let's assume n = 8 * 10^28 electrons per cubic meter.
Now, substituting the values into the drift velocity formula to find the electric current (I):
1.5 * 10^(-5) = 10.4 / (8 * 10^28 * 1.963495408 * 10^(-5) * 1.6 * 10^(-19))
Solving this equation will give us the electric current, I.
Once we have the electric current, we can calculate the total charge (Q) passing through the wire using the formula Q = I * Δt. The value of Δt needs to be given or assumed. Let's assume Δt = 1 second for this calculation.
Finally, we can calculate the number of electrons (Ne) passing through the point:
Ne = Q / e
Remember that the value of n assumed and the value of Δt chosen will affect the accuracy of the final result.