copper has 8.5 x 10^28 electrons per cubic meter. (a) how many electrons are there in 30 cm length a 12 gauge copper wire (diameter 2.05 mm)? (b) if a current of 1.55 A is flowing in the wire, what is the average drift speed of the electrons along the wire? (There are 6.24 x 10^18 electrons in 1 coulomb of charge.)

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To calculate the number of electrons in a 30 cm length of a 12 gauge copper wire, we first need to determine the volume of the wire.

Step 1: Calculate the cross-sectional area of the wire
The diameter of the wire is given as 2.05 mm. We can use this to find the radius and then calculate the cross-sectional area.

Radius = diameter/2 = 2.05 mm/2 = 1.025 mm = 0.001025 m
Area = π * radius^2 = π * (0.001025 m)^2

Step 2: Calculate the volume of the wire
The volume of a cylinder (wire) is given by multiplying the cross-sectional area with the length of the wire.

Volume = Area * Length = (π * (0.001025 m)^2) * 0.3 m

Step 3: Calculate the number of electrons
The number of electrons can be determined by multiplying the volume of the wire by the number of electrons per cubic meter of copper.

Number of electrons = Volume * Number of electrons per cubic meter

Now, let's plug in the values and calculate the number of electrons:

Number of electrons = [(π * (0.001025 m)^2) * 0.3 m] * (8.5 x 10^28 electrons/m^3)

For part (b), to calculate the average drift speed of electrons, we need to use the equation:

Drift speed = Current / (Number of electrons / Charge per Coulomb)

We are given that the current is 1.55 A, and there are 6.24 x 10^18 electrons in 1 coulomb of charge.

Drift speed = 1.55 A / (Number of electrons / 6.24 x 10^18 electrons/C)

Now, plug in the calculated number of electrons from part (a) and calculate the drift speed.