Two parallel conductors `A` and `B` of equal lengths carry currents `I` and `10 I`, respectively, in the same direction. Then

Options

A. A and B will repel each other with same force
B. A and B with attract each other with same force
C. A will attract B but B will repel A
D. A and B will attract each other with different forces

Answer

To solve the problem regarding the two parallel conductors A and B carrying currents I and 10I respectively in the same direction, we will follow these steps:

### Step 1: Understand the Concept of Magnetic Force Between Parallel Conductors
When two parallel conductors carry currents, they exert forces on each other. The direction of the force depends on the direction of the currents. If the currents are in the same direction, the conductors will attract each other.

### Step 2: Identify the Currents in the Conductors
We have:
- Current in conductor A, \( I_A = I \)
- Current in conductor B, \( I_B = 10I \)

### Step 3: Use the Formula for the Magnetic Force Between Two Parallel Conductors
The force per unit length \( F/L \) between two parallel conductors separated by a distance \( r \) is given by the formula:
\[ \frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{I_A I_B}{r} \]
Where:
- \( \mu_0 \) is the permeability of free space.
- \( I_A \) and \( I_B \) are the currents in the conductors.
- \( r \) is the distance between the conductors.

### Step 4: Substitute the Values into the Formula
Substituting the values of the currents into the formula:
\[ \frac{F}{L} = \frac{\mu_0}{2\pi} \cdot \frac{I \cdot 10I}{r} = \frac{10\mu_0 I^2}{2\pi r} \]

### Step 5: Analyze the Result
The force per unit length \( F/L \) is positive, which indicates that the force is attractive. Since both conductors carry current in the same direction, they will attract each other.

### Conclusion
Thus, the two parallel conductors A and B will attract each other due to the magnetic forces acting between them.