Two power lines run parallel for a distance of 254 m and are separated by a distance of 40.0 cm. If the current in each of the two lines is 140 A and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other.

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16-03-2020
Physics

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Two power lines run parallel for a distance of 254 m and are separated by a distance of 40.0 cm. If the current in each of the two lines is 140 A and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other.

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cjmejiab cjmejiab · Answer 1 · 2020-03-19T06:29:41+01:00

To solve this problem we will apply the concepts related to the electromagnetic force given between two cables. For this purpose we will consider the following mathematical relation,

[tex]F = \frac{\mu_0I_1I_2L}{(2\pi d)}[/tex]

Here,

[tex]\mu_0[/tex] = Permeability at free space

[tex]I_{1,2}[/tex] = Current

L = Length

d = Distance between them

With our values we have,

[tex]F = \frac{(4\pi*10^{-7}) (140)(140) (254)}{(2\pi (40*10^{-2}))}[/tex]

[tex]F = 2.4892N[/tex]

Therefore the force between the wires is 2.4892 N as the current flows in oposite direction, the force is away from each other.