Calculate the force per unit length acting between two parallel wires of infinite extent separated by distance 2cm and each carry in 4 amperes?

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Answer

< b='' /> Calculation of Force per Unit Length between Two Parallel Wires < />

Given Information: < 2='' />
- Distance between the wires (d) = 2 cm = 0.02 m
- Current in each wire (I) = 4 A

Formula: < 2='' />
The force per unit length (F) between two parallel wires can be calculated using the formula:

F = (μ₀ * I₁ * I₂) / (2 * π * d)

where:
- F is the force per unit length
- μ₀ is the permeability of free space (4π × 10^-7 T·m/A)
- I₁ and I₂ are the currents in the two wires
- d is the distance between the wires

Calculation: < 2='' />
Substituting the given values into the formula:

F = (4π × 10^-7 T·m/A * 4 A * 4 A) / (2 * π * 0.02 m)

Simplifying the equation:

F = (4π × 10^-7 T·m/A * 16 A²) / (2 * π * 0.02 m)

F = (8π × 10^-7 T·m) / (0.04 m)

F = 200π × 10^-7 T·m/m

F ≈ 6.28 × 10^-6 T·m/m

Final Answer: < 2='' />
The force per unit length between the two parallel wires is approximately 6.28 × 10^-6 T·m/m.

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