A copper wire has a square cross-section, 2.0 mm on a side. It carries a current of 8 A and the density of free electrons is `8 xx 10^(28)m^(-3)`. The drift speed of electrons is equal to

Explanation

To find the drift speed of electrons in a copper wire, we can use the formula:

\[ v_d = \frac{I}{n \cdot A \cdot e} \]

where:
- \( v_d \) is the drift speed,
- \( I \) is the current (in Amperes),
- \( n \) is the density of free electrons (in \( m^{-3} \)),
- \( A \) is the cross-sectional area of the wire (in \( m^2 \)),
- \( e \) is the charge of an electron (\( 1.6 \times 10^{-19} \) Coulombs).

### Step 1: Calculate the cross-sectional area \( A \)

The wire has a square cross-section with a side length of \( 2.0 \, \text{mm} \). First, we need to convert this to meters:

\[ 2.0 \, \text{mm} = 2.0 \times 10^{-3} \, \text{m} \]

Now, calculate the area:

\[ A = \text{side}^2 = (2.0 \times 10^{-3})^2 = 4.0 \times 10^{-6} \, \text{m}^2 \]

### Step 2: Substitute the values into the formula

Now we can substitute the known values into the drift speed formula:

- Current \( I = 8 \, \text{A} \)
- Density of free electrons \( n = 8 \times 10^{28} \, \text{m}^{-3} \)
- Area \( A = 4.0 \times 10^{-6} \, \text{m}^2 \)
- Charge of an electron \( e = 1.6 \times 10^{-19} \, \text{C} \)

Substituting these values into the formula gives:

\[ v_d = \frac{8}{(8 \times 10^{28}) \cdot (4.0 \times 10^{-6}) \cdot (1.6 \times 10^{-19})} \]

### Step 3: Calculate the denominator

First, calculate the denominator:

\[ (8 \times 10^{28}) \cdot (4.0 \times 10^{-6}) \cdot (1.6 \times 10^{-19}) = 8 \times 4.0 \times 1.6 \times 10^{28 - 6 - 19} \]

Calculating the numerical part:

\[ 8 \times 4.0 = 32 \]
\[ 32 \times 1.6 = 51.2 \]

Now for the powers of ten:

\[ 10^{28 - 6 - 19} = 10^{3} \]

So the denominator is:

\[ 51.2 \times 10^{3} = 51200 \]

### Step 4: Calculate the drift speed \( v_d \)

Now we can calculate \( v_d \):

\[ v_d = \frac{8}{51200} = 0.00015625 \, \text{m/s} \]

This can be expressed in scientific notation:

\[ v_d = 1.5625 \times 10^{-4} \, \text{m/s} \]

### Final Answer

Thus, the drift speed of electrons in the copper wire is approximately:

\[ v_d \approx 0.156 \times 10^{-3} \, \text{m/s} \]