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.
current=driftevelocity*area*electrondensity
but number electrons per lenth=electron dinsity)*area
To calculate the number of free electrons per meter length of wire, we can use the formula:
n = I / (Q * E * A * v * t)
Where:
n = number of free electrons per meter length of wire
I = current (amps)
Q = net charge on the object (coulombs)
E = elementary charge (coulombs)
A = cross-sectional area of the wire (square meters)
v = drift velocity (meters per second)
t = time (seconds)
Now let's break down the question into the given information and apply it to the formula:
Given:
I = 2.0A
v = 1.0 x 10^-3 m/s
Step 1: Determine the other variables needed for the formula.
We need to find the values of Q, E, and A for the wire. The value of Q depends on the material and its conductivity, while E is the charge of a single electron.
Step 2: Determine the net charge on the wire (Q).
To calculate Q, we need to know the net charge on the wire. This information is not provided in the question. However, for a typical wire, the net charge can be assumed to be zero since the wire is electrically neutral.
Q = 0 C
Step 3: Determine the elementary charge (E).
The elementary charge is the charge of a single electron. Its value is approximately 1.6 x 10^-19 coulombs.
E = 1.6 x 10^-19 C
Step 4: Determine the cross-sectional area of the wire (A).
The cross-sectional area of the wire can vary depending on its dimensions. Assuming a round wire, the cross-sectional area (A) can be calculated using the formula:
A = π * r^2
where r is the radius of the wire.
If the radius of the wire is not given, we won't be able to calculate the exact value of A. However, we can assume a reasonable value based on typical wire dimensions. Let's assume a radius of 1mm, which is equal to 0.001 meters.
A = π * (0.001)^2 = π * 0.000001 square meters
Step 5: Calculate the number of free electrons per meter length of wire (n).
Substituting the values into the formula:
n = I / (Q * E * A * v * t)
= 2.0 / (0 * 1.6 x 10^-19 * π * 0.000001 * 1.0 x 10^-3 * t)
= 2.0 / (π * 1.6 x 10^-19 * 0.000001 * t)
Since the time (t) is not provided in the question, we cannot determine the exact value of n without that information. However, you can substitute the value of t into the equation to get the value of n for a specific time duration. Just remember to use consistent units throughout the calculation.
By following these steps, you can calculate the number of free electrons per meter length of wire. Remember, the calculations may vary depending on the given information and assumptions made.