Two parallel wires carry current of 1.6 ka in opposite directions. the distance between the wires is r=1.6 m compute the magnitude of the force per unit length exerted by one wire on the other?
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To compute the magnitude of the force per unit length exerted by one wire on the other, we can use the formula for the magnetic force between two parallel current-carrying wires. According to Ampere's Law, the force per unit length (F/l) between the wires can be calculated using the formula:
F/l = μ₀ * I₁ * I₂ * L / (2πr)
Where:
F/l = Force per unit length
μ₀ = Permeability of free space (4π × 10⁻⁷ T·m/A)
I₁, I₂ = Current in the two wires
L = Length of the wire segment
r = Distance between the wires
Given:
Current in each wire (I₁ and I₂) = 1.6 kA = 1.6 × 10³ A
Distance between the wires (r) = 1.6 m
We need the length of the wire segment (L) to calculate the force per unit length. However, since the length is not provided in the question, we'll consider it as an arbitrary length of 1 meter for simplicity. You can substitute any other value if a specific length is given.
Now, we can substitute the given values into the formula:
F/l = (4π × 10⁻⁷ T·m/A) * (1.6 × 10³ A) * (1.6 × 10³ A) * (1 m) / (2π * 1.6 m)
Simplifying the equation:
F/l = (4π × 10⁻⁷ * 1.6 × 10³ * 1.6 × 10³) / (2π * 1.6)
F/l ≈ (4 × 1.6 × 1.6) / (2 * 1.6 × 10⁻⁷)
F/l ≈ (6.4 / 3.2 × 10⁻⁷)
F/l ≈ 2 × 10⁸ N/m
Therefore, the magnitude of the force per unit length exerted by one wire on the other is approximately 2 × 10⁸ N/m.