The perpendicular distance between two conductor of 12 m each is 0.15cm. They carry 300A in same direction. The force acti ng between them is

Options

A. 288N repulsion
B. 144N attraction
C. 14N attraction
D. 36N repulsion

Answer

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

### Step 1: Understand the Given Data
- Length of each conductor, \( L = 12 \, \text{m} \)
- Current in each conductor, \( I_1 = I_2 = 300 \, \text{A} \)
- Perpendicular distance between the conductors, \( r = 0.15 \, \text{cm} = 0.0015 \, \text{m} \)

### Step 2: Use the Formula for the Force Between Two Parallel Conductors
The force per unit length between two parallel conductors carrying currents is given by the formula:
\[ F = \frac{\mu_0 I_1 I_2 L}{2 \pi r} \]
where:
- \( F \) is the total force between the conductors,
- \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) (the permeability of free space),
- \( I_1 \) and \( I_2 \) are the currents in the conductors,
- \( L \) is the length of the conductors,
- \( r \) is the distance between the conductors.

### Step 3: Substitute the Values into the Formula
Substituting the known values into the formula:
\[ F = \frac{(4\pi \times 10^{-7}) \times (300) \times (300) \times (12)}{2 \pi \times (0.0015)} \]

### Step 4: Simplify the Expression
1. Cancel \( \pi \) from the numerator and denominator:
\[ F = \frac{(4 \times 10^{-7}) \times (300) \times (300) \times (12)}{2 \times (0.0015)} \]
2. Calculate the numerator:
\[ F = \frac{(4 \times 10^{-7}) \times (90000) \times (12)}{2 \times (0.0015)} \]
\[ = \frac{(4 \times 10^{-7}) \times (1080000)}{0.003} \]
\[ = \frac{4320000 \times 10^{-7}}{0.003} \]
\[ = 144 \, \text{N} \]

### Step 5: Determine the Nature of the Force
Since both conductors carry current in the same direction, the force between them is attractive.

### Final Answer
The force acting between the two conductors is \( 144 \, \text{N} \) and it is attractive.

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