A metallic wire carries a current of 100 A , its area of cross section is `1 cm^(2)`. If the resistivity of the copper is `1.7xx10^(-8) Omega m`, then the electric field strength in the copper will be

Options

A. `1.7xx10^(-2)V//m`
B. `2.7xx10^(-2)V//m`
C. `1.7xx10^(-3)V//m`
D. `2.7xx10^(-3)V//m`

Explanation

To find the electric field strength in the copper wire, we can follow these steps:

### Step 1: Understand the relationship between electric field (E), voltage (V), and length (L)
The electric field strength (E) in a conductor can be expressed as:
\[ E = \frac{V}{L} \]
Where:
- \( E \) is the electric field strength (in volts per meter, V/m)
- \( V \) is the voltage across the conductor (in volts)
- \( L \) is the length of the conductor (in meters)

### Step 2: Relate voltage (V) to current (I) and resistance (R)
The voltage across the conductor can also be expressed using Ohm's law:
\[ V = I \cdot R \]
Where:
- \( I \) is the current (in amperes, A)
- \( R \) is the resistance (in ohms, Ω)

### Step 3: Express resistance (R) in terms of resistivity (ρ), length (L), and area (A)
The resistance of a conductor can be calculated using the formula:
\[ R = \frac{\rho L}{A} \]
Where:
- \( \rho \) is the resistivity of the material (in ohm-meters, Ω·m)
- \( A \) is the cross-sectional area of the conductor (in square meters, m²)

### Step 4: Substitute the expression for resistance (R) into the voltage equation
Substituting the expression for \( R \) into \( V = I \cdot R \):
\[ V = I \cdot \frac{\rho L}{A} \]

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

### Step 6: Plug in the values
We know:
- \( I = 100 \, A \)
- \( \rho = 1.7 \times 10^{-8} \, \Omega \cdot m \)
- \( A = 1 \, cm^2 = 1 \times 10^{-4} \, m^2 \)

Now substituting these values into the equation:
\[ E = \frac{100 \cdot (1.7 \times 10^{-8})}{1 \times 10^{-4}} \]

### Step 7: Calculate the electric field strength
Calculating the above expression:
\[ E = \frac{1.7 \times 10^{-6}}{1 \times 10^{-4}} \]
\[ E = 1.7 \times 10^{-2} \, V/m \]

### Final Answer
The electric field strength in the copper wire is:
\[ E = 1.7 \times 10^{-2} \, V/m \]

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