A cooper wire has a diameter of 1.02 mm and carries a constant current of 1.67 A. If density of free electron in copper is 8.5×10^28 m-3 calculates the current density and the drift velocity of the electron
To find the current density and drift velocity of electrons in the copper wire, we can use the formula:
J = n * e * v_d
where:
J is the current density (in A/m^2),
n is the density of free electrons in copper (in m^-3),
e is the charge of an electron (approximately -1.6 x 10^-19 C),
and v_d is the drift velocity of electrons (in m/s).
First, let's calculate the current density. We know that the current is 1.67 A and the diameter of the wire is 1.02 mm. The cross-sectional area (A) can be calculated using the formula:
A = π * r^2
where r is the radius of the wire (diameter divided by 2):
r = 1.02 mm / 2 = 0.51 mm = 0.51 x 10^-3 m
Now, we can calculate the cross-sectional area:
A = π * (0.51 x 10^-3 m)^2
Next, we'll calculate the current density using the formula:
J = I / A
where I is the current:
J = 1.67 A / A
Now, let's calculate the drift velocity. We know the current density (J) and the density of free electrons (n). Rearranging the formula, we have:
J = n * e * v_d
Solving for v_d, we get:
v_d = J / (n * e)
Now, substitute the values of J, n, and e to calculate the drift velocity.
Finally, we have the current density (J) and the drift velocity (v_d) of the electrons in the copper wire.
Note: Remember to convert the final answer to the appropriate units based on the question requirements.