What is the drift velocity of electrons in a copper conductor having a cross-sectional area of `5xx10^(-6) m^(2)` if the current is 10 A. Assume there are `8.0xx10^(28) "electrons"//m^(3)`.

Answer

To find the drift velocity of electrons in a copper conductor, we can use the formula for current:

\[ I = n \cdot A \cdot e \cdot v_d \]

Where:
- \( I \) is the current (in Amperes)
- \( n \) is the number of charge carriers per unit volume (in \( m^{-3} \))
- \( A \) is the cross-sectional area (in \( m^{2} \))
- \( e \) is the charge of an electron (approximately \( 1.6 \times 10^{-19} \) Coulombs)
- \( v_d \) is the drift velocity (in \( m/s \))

Given:
- \( I = 10 \, A \)
- \( A = 5 \times 10^{-6} \, m^{2} \)
- \( n = 8.0 \times 10^{28} \, electrons/m^{3} \)

### Step 1: Rearrange the formula to solve for drift velocity \( v_d \)

We can rearrange the formula to isolate \( v_d \):

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

### Step 2: Substitute the known values into the equation

Now, substitute the known values into the equation:

\[ v_d = \frac{10}{(8.0 \times 10^{28}) \cdot (5 \times 10^{-6}) \cdot (1.6 \times 10^{-19})} \]

### Step 3: Calculate the denominator

First, calculate the denominator:

1. Calculate \( n \cdot A \):
\[ n \cdot A = (8.0 \times 10^{28}) \cdot (5 \times 10^{-6}) = 4.0 \times 10^{23} \]

2. Now, multiply by \( e \):
\[ n \cdot A \cdot e = (4.0 \times 10^{23}) \cdot (1.6 \times 10^{-19}) = 6.4 \times 10^{4} \]

### Step 4: Calculate drift velocity \( v_d \)

Now substitute back into the equation for \( v_d \):

\[ v_d = \frac{10}{6.4 \times 10^{4}} \]

Calculating this gives:

\[ v_d \approx 1.5625 \times 10^{-5} \, m/s \]

### Step 5: Round the result

Rounding to two decimal places, we find:

\[ v_d \approx 1.56 \, m/s \]

### Final Answer

The drift velocity of electrons in the copper conductor is approximately \( 1.56 \, m/s \).

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