Find the true statement.a)The force between two parallel current carrying wires is independent of the radii of the wiresb)The force between two parallel current carrying wires is independent of the length of the wiresc)The force between two parallel current carrying wires is independent of the magnitude of currentsd)The force between two parallel current carrying wires is independent of their distance of separationCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

The force between two parallel current carrying wires is independent of the radii of the wires.
From Ampere’s circuital law, the magnitude of the field due to the first conductor can be given by:

The force between the parallel plates is given by:

From this equation, we understand that the force between the parallel current carrying wires does not depend on the ‘radii’.

Answer

Statement: The force between two parallel current carrying wires is independent of the radii of the wires.

Explanation:
When two parallel current-carrying wires are placed close to each other, they experience a magnetic force due to the interaction of their magnetic fields. This force is given by the formula:

F = (μ₀ * I₁ * I₂ * L) / (2π * d)

Where:
F is the force between the wires,
μ₀ is the permeability of free space (a constant),
I₁ and I₂ are the magnitudes of the currents in the wires,
L is the length of the wires, and
d is the distance of separation between the wires.

To understand why the force between the wires is independent of the radii of the wires, let's consider the factors in the above formula:

1. Permeability of free space (μ₀):
The permeability of free space is a constant value and is independent of the radii of the wires. Therefore, it does not affect the dependence of the force on the radii.

2. Current magnitudes (I₁ and I₂):
The magnitudes of the currents flowing through the wires determine the strength of the magnetic fields generated by the wires. These currents are independent of the radii of the wires. Hence, the force between the wires is not influenced by the radii.

3. Length of the wires (L):
The length of the wires affects the overall magnetic field produced by each wire, but it does not affect the force between the wires. The force is determined by the interaction of the magnetic fields, which depends on the distance of separation between the wires, not their lengths.

4. Distance of separation (d):
The distance between the wires is a crucial factor that determines the force between them. As the distance increases, the force decreases, and vice versa. The force is inversely proportional to the distance of separation and is independent of the radii of the wires.

Therefore, from the above analysis, we can conclude that the force between two parallel current carrying wires is indeed independent of the radii of the wires (Option A is correct).

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