A power line lies along the east-west direction and carries a current of 10 ampere. The force per metre due to the earth's magnetic field of `10^(-4)` tesla is

Options

A. `10^(-5) N`
B. `10^(-4) N`
C. `10^(-3) N`
D. `10^(-2) N`

Explanation

To find the force per meter on a power line carrying a current in the presence of a magnetic field, we can use the formula for the magnetic force on a current-carrying conductor. The formula is given by:

\[ F = I \cdot L \cdot B \cdot \sin(\theta) \]

Where:
- \( F \) is the force,
- \( I \) is the current,
- \( L \) is the length of the conductor,
- \( B \) is the magnetic field strength, and
- \( \theta \) is the angle between the direction of the current and the magnetic field.

### Step-by-step Solution:

1. **Identify the Given Values:**
- Current \( I = 10 \, \text{A} \)
- Magnetic field \( B = 10^{-4} \, \text{T} \)
- The angle \( \theta = 90^\circ \) (since the current flows east-west and the magnetic field is vertical).

2. **Calculate the Sine of the Angle:**
- Since \( \theta = 90^\circ \), we have:
\[ \sin(90^\circ) = 1 \]

3. **Substitute Values into the Formula:**
- The force per unit length \( \frac{F}{L} \) can be expressed as:
\[ \frac{F}{L} = I \cdot B \cdot \sin(\theta) \]
- Substituting the known values:
\[ \frac{F}{L} = 10 \, \text{A} \cdot 10^{-4} \, \text{T} \cdot 1 \]

4. **Perform the Calculation:**
- Calculate the force per meter:
\[ \frac{F}{L} = 10 \cdot 10^{-4} = 10^{-3} \, \text{N/m} \]

5. **Final Answer:**
- The force per meter due to the earth's magnetic field is:
\[ \frac{F}{L} = 10^{-3} \, \text{N/m} \]

### Conclusion:
The correct answer is \( 10^{-3} \, \text{N/m} \).