The magnitude of the force between a pair of conductors, each of length 110 cm, carrying a current of 10A and seperated by a distance of 10 cm is

Options

A. `55xx 10^(-5) N`
B. `44 xx 10^(-5) N`
C. ` 33 xx 10^(-5) N`
D. ` 22 xx 10^(-5) N`

Explanation

To solve the problem of finding the magnitude of the force between two parallel conductors carrying current, we can follow these steps:

### Step 1: Identify the given values
- Length of the conductors, \( l = 110 \, \text{cm} = 1.1 \, \text{m} \) (conversion from cm to m)
- Current in each conductor, \( I_1 = I_2 = 10 \, \text{A} \)
- Distance between the conductors, \( d = 10 \, \text{cm} = 0.1 \, \text{m} \) (conversion from cm to m)

### Step 2: Use the formula for the force per unit length between two parallel conductors
The formula for the force per unit length \( \frac{F}{l} \) between two parallel conductors is given by:
\[ \frac{F}{l} = \frac{\mu_0}{2\pi} \cdot \frac{I_1 I_2}{d} \]
where \( \mu_0 \) (the permeability of free space) is approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \).

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ \frac{F}{l} = \frac{4\pi \times 10^{-7}}{2\pi} \cdot \frac{10 \cdot 10}{0.1} \]

### Step 4: Simplify the equation
- The \( \pi \) terms cancel out:
\[ \frac{F}{l} = \frac{4 \times 10^{-7}}{2} \cdot \frac{100}{0.1} \]
- Simplifying further:
\[ \frac{F}{l} = 2 \times 10^{-7} \cdot 1000 = 2 \times 10^{-7} \cdot 10^3 = 2 \times 10^{-4} \, \text{N/m} \]

### Step 5: Calculate the total force \( F \)
Now, we can find the total force \( F \) by multiplying the force per unit length by the length of the conductors:
\[ F = \left(2 \times 10^{-4}\right) \cdot 1.1 = 2.2 \times 10^{-4} \, \text{N} \]

### Step 6: Final Result
Thus, the magnitude of the force between the two conductors is:
\[ F = 2.2 \times 10^{-4} \, \text{N} = 22 \times 10^{-5} \, \text{N} \]

### Conclusion
The final answer is \( 22 \times 10^{-5} \, \text{N} \).

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