A copper wire of cross sectional area 2.0 `mm^(2)`, resistivity `=1.7xx10^(-8)Omegam`, carries a current of 1 A. The electric field in the copper wire is

Options

A. `8.5xx10^(-5)(V)/(m)`
B. `8.5xx10^(-4)(V)/(m)`
C. `8.5xx10^(-3)(V)/(m)`
D. `8.5xx10^(-2)(V)/(m)`

Explanation

To find the electric field in a copper wire carrying a current of 1 A, we can follow these steps:

### Step 1: Understand the relationship between electric field (E), voltage (V), and distance (d)
The electric field (E) in a conductor can be expressed as:
\[ E = \frac{V}{L} \]
where \( V \) is the voltage across the length \( L \) of the conductor.

### Step 2: Relate voltage (V) to current (I) and resistance (R)
Using Ohm's law, the voltage (V) can be expressed as:
\[ V = I \cdot R \]
where \( I \) is the current flowing through the wire and \( R \) is the resistance of the wire.

### Step 3: Calculate the resistance (R) of the copper wire
The resistance (R) of a wire can be calculated using the formula:
\[ R = \rho \frac{L}{A} \]
where:
- \( \rho \) is the resistivity of the material (for copper, \( \rho = 1.7 \times 10^{-8} \, \Omega \cdot m \)),
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.

Given that the cross-sectional area \( A = 2.0 \, mm^2 = 2.0 \times 10^{-6} \, m^2 \).

### Step 4: Substitute the resistance into the voltage equation
Now we can substitute the expression for resistance into the voltage equation:
\[ V = I \cdot R = I \cdot \left( \rho \frac{L}{A} \right) \]
Thus, we have:
\[ V = I \cdot \rho \frac{L}{A} \]

### Step 5: Substitute V into the electric field equation
Now substitute \( V \) into the electric field equation:
\[ E = \frac{I \cdot \rho \frac{L}{A}}{L} \]
This simplifies to:
\[ E = \frac{I \cdot \rho}{A} \]

### Step 6: Plug in the values
Now we can substitute the known values:
- \( I = 1 \, A \),
- \( \rho = 1.7 \times 10^{-8} \, \Omega \cdot m \),
- \( A = 2.0 \times 10^{-6} \, m^2 \).

Thus,
\[ E = \frac{1 \cdot (1.7 \times 10^{-8})}{2.0 \times 10^{-6}} \]

### Step 7: Calculate the electric field
Calculating the above expression:
\[ E = \frac{1.7 \times 10^{-8}}{2.0 \times 10^{-6}} = 0.0085 \, V/m = 8.5 \times 10^{-3} \, V/m \]

### Final Result
The electric field in the copper wire is:
\[ E = 8.5 \times 10^{-3} \, V/m \]