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two power lines run parallel for a distance of 269 m and are separated by a distance of 40.0 cm. if the current in each of the two lines is 120 a and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other.

User Khiet
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Answer: To determine the magnitude and direction of the force each wire exerts on the other, we can use the formula for the magnetic force between two parallel conductors:

F = μ₀ * I₁ * I₂ * L / (2πd)

where F is the magnitude of the force, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I₁ and I₂ are the currents in the two conductors, L is the length of the conductors that are parallel to each other, and d is the distance between the two conductors.

In this case, we have:

I₁ = I₂ = 120 A

L = 269 m

d = 0.40 m

Substituting these values into the formula, we get:

F = 4π × 10⁻⁷ T·m/A * 120 A * 120 A * 269 m / (2π * 0.40 m)

= 4π × 10⁻⁷ * 120² * 269 / 0.80

= 1.234 N

Therefore, the magnitude of the force each wire exerts on the other is 1.234 N.

To determine the direction of the force, we can use the right-hand rule. If we point the thumb of our right hand in the direction of the current in the first wire, and the fingers of our right hand in the direction of the current in the second wire, then the direction of the force will be perpendicular to the plane defined by the two currents, and will be given by the direction of our extended palm. If the force on the first wire is F₁, and the force on the second wire is F₂, then we have:

F₁ = -F₂

where the negative sign indicates that the two forces are in opposite directions. Therefore, the force on the first wire is directed towards the second wire, and the force on the second wire is directed towards the first wire.

User Ibrahim Hussein
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