find the total momentum of electrons in a straight wire of lenght 1000m carrying a current of 70A.
electron momentum in length L of wire =
I*(m/e)*L
where I is the current flowing, m is the electron mass and e is the electron charge.
= 70 C/s*9.81*10^-^31 kg*1000 m
/1.6*10^-19C
= 4.3*10^-7 kg m/s
sir very-very helpful thanks a lot......
To find the total momentum of electrons in a straight wire, first, we need to determine the number of electrons in the wire.
The formula to calculate the number of electrons is:
Number of electrons = (Current * Time) / (Charge of an electron)
The charge of an electron is approximately 1.6 × 10^-19 Coulombs.
Let's assume the time is 1 second.
Number of electrons = (70A * 1s) / (1.6 × 10^-19 C)
Number of electrons ≈ 4.375 × 10^19
Since each electron has a momentum equal to its mass multiplied by its velocity, we need to calculate the velocity of the electrons.
The formula for the velocity of electrons is:
Velocity = (Current * Charge of an electron) / (Number of electrons * Cross-sectional area * Charge density)
The cross-sectional area and charge density values are not provided, so we cannot calculate the exact velocity of the electrons. However, we can assume an average velocity based on common values.
For example, assuming a cross-sectional area of 1 mm^2 and a charge density of 10^29 electrons/m^3, we can calculate:
Velocity = (70A * 1.6 × 10^-19 C) / (4.375 × 10^19 * 1 mm^2 * 10^29 electrons/m^3)
Velocity ≈ 0.255 m/s
Now, we can calculate the mass of a single electron, which is approximately 9.1 × 10^-31 kg.
Finally, we can calculate the total momentum of electrons in the wire using the formula:
Total momentum = Number of electrons * Mass of an electron * Velocity
Total momentum ≈ (4.375 × 10^19) * (9.1 × 10^-31 kg) * (0.255 m/s)
The exact value of the total momentum will depend on the actual values of the cross-sectional area and charge density, as well as the specific characteristics of the wire.
To find the total momentum of electrons in a straight wire, we need to use the formula:
Momentum (p) = mass (m) × velocity (v)
Now, the mass of an electron (m) is approximately 9.11 x 10^-31 kg.
To calculate the velocity of electrons (v) in the wire, we can use Ohm's Law, which states that the current (I) flowing through a wire is equal to the charge (Q) passing through it divided by the time (t) taken:
I = Q / t
The charge passing through a wire can be calculated using the formula:
Q = I × t
Here, I is the current (in Amperes) and t is the time (in seconds).
Given that the current in the wire is 70A, and the length of the wire is 1000m (which we can assume as the time taken for the charge to pass through the wire), we can now find the charge (Q):
Q = I × t
= 70A × 1000s
= 70000 C
Now that we have the charge (Q), we can find the velocity of the electrons (v) using the formula:
v = Q / (n × e)
Where:
- n is the number of electrons per unit volume (m^3) of the wire, which is given by:
n = density (ρ) / (molecular mass (M) x Avogadro's constant (N))
- e is the elementary charge, which is approximately 1.6 x 10^-19 C.
The density of a material typically used for wires, such as copper, is around 8.96 x 10^3 kg/m^3. The molecular mass of copper is 63.55 g/mol, and Avogadro's constant is 6.022 x 10^23 particles/mol.
Plugging in the values, we can calculate n:
n = ρ / (M × N)
= (8.96 x 10^3 kg/m^3) / (63.55 g/mol × 6.022 x 10^23 particles/mol)
= 8.96 x 10^3 kg/m^3 / (63.55 g/mol × 6.022 x 10^23 particles/mol)
≈ 8.48 x 10^28 electrons/m^3
Now we can find the velocity:
v = Q / (n × e)
= 70000 C / (8.48 x 10^28 electrons/m^3 × 1.6 x 10^-19 C/electron)
= 70000 C / (8.48 x 10^9 electrons × 1.6 x 10^-19 C/electron)
≈ 5.21 x 10^-20 m/s
Finally, we can calculate the total momentum (p) using the formula:
p = m × v
= 9.11 x 10^-31 kg × 5.21 x 10^-20 m/s
≈ 4.75 x 10^-50 kg·m/s
Therefore, the total momentum of the electrons in the straight wire is approximately 4.75 x 10^-50 kg·m/s.