When 115V is applied across a wire that is 10m long and has a 0.30mm radius, the current density is `1.4xx10^(4) A//m^(2)`. The resistivity of the wire is

Options

A. `2.0xx10^(-4)Omegam`
B. `4.1xx10^(-4)Omegam`
C. `8.2xx10^(-4)Omega m`
D. `2.0xx10^(-3)Omegam`

Explanation

To find the resistivity of the wire, we will follow these steps:

### Step 1: Identify the given values
- Voltage (V) = 115 V
- Length of the wire (L) = 10 m
- Current density (J) = 1.4 × 10^4 A/m²

### Step 2: Calculate the electric field (E)
The electric field (E) can be calculated using the formula:
\[ E = \frac{V}{L} \]
Substituting the known values:
\[ E = \frac{115 \, \text{V}}{10 \, \text{m}} = 11.5 \, \text{V/m} \]

### Step 3: Use the relationship between current density (J), electric field (E), and resistivity (ρ)
The relationship is given by:
\[ J = \frac{E}{\rho} \]
Rearranging this formula to find resistivity (ρ):
\[ \rho = \frac{E}{J} \]

### Step 4: Substitute the values of E and J into the formula
Now we can substitute the values we calculated:
\[ \rho = \frac{11.5 \, \text{V/m}}{1.4 \times 10^4 \, \text{A/m²}} \]

### Step 5: Calculate the resistivity (ρ)
Perform the calculation:
\[ \rho = \frac{11.5}{1.4 \times 10^4} \]
\[ \rho = \frac{11.5}{14000} \]
\[ \rho \approx 8.21 \times 10^{-4} \, \Omega \cdot \text{m} \]

### Step 6: Final Result
Thus, the resistivity of the wire is approximately:
\[ \rho \approx 8.2 \times 10^{-4} \, \Omega \cdot \text{m} \]