Two straight wires each 10 cm long are parallel to one another and separated by 2 cm. when the current flowing in them is 30 A and 40 A respectively then the force experienced by either of the wires is

Options

A. `1.2xx10^(-3)N`
B. `12xx10^(-3)N`
C. `11.2xx10^(-3)N`
D. `10.2xx10^(-3)N`

Answer

To solve the problem of finding the force experienced by either of the two parallel wires carrying currents, we can follow these steps:

### Step 1: Understand the Given Data
We have two wires:
- Length of each wire, \( L = 10 \, \text{cm} = 0.1 \, \text{m} \)
- Separation between the wires, \( R = 2 \, \text{cm} = 0.02 \, \text{m} \)
- Current in the first wire, \( I_1 = 30 \, \text{A} \)
- Current in the second wire, \( I_2 = 40 \, \text{A} \)

### Step 2: Use the Formula for the Force Between Two Parallel Current-Carrying Wires
The force per unit length between two parallel wires carrying currents can be calculated using the formula:

\[ F = \frac{\mu_0 I_1 I_2 L}{2 \pi R} \]

where:
- \( \mu_0 \) is the permeability of free space, \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \)

### Step 3: Substitute the Values into the Formula
Substituting the known values into the formula:

\[ F = \frac{(4\pi \times 10^{-7}) \times (30) \times (40) \times (0.1)}{2 \pi \times (0.02)} \]

### Step 4: Simplify the Expression
1. Cancel \( \pi \) from the numerator and denominator:

\[ F = \frac{4 \times 10^{-7} \times 30 \times 40 \times 0.1}{2 \times 0.02} \]

2. Calculate the denominator:

\[ 2 \times 0.02 = 0.04 \]

3. Now substitute this back into the equation:

\[ F = \frac{4 \times 10^{-7} \times 30 \times 40 \times 0.1}{0.04} \]

### Step 5: Calculate the Numerator
Calculating the numerator:

\[ 4 \times 30 \times 40 \times 0.1 = 480 \]

### Step 6: Final Calculation
Now substitute the numerator back into the equation:

\[ F = \frac{480 \times 10^{-7}}{0.04} \]

Calculating \( \frac{480}{0.04} = 12000 \):

\[ F = 12000 \times 10^{-7} = 1.2 \times 10^{-3} \, \text{N} \]

### Conclusion
The force experienced by either of the wires is:

\[ F = 1.2 \times 10^{-3} \, \text{N} \]