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Magnetic field and magnetic force between wires

  1. Jan 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Electricity from the power plant with a power P = 100MW is transmitted by V= 220kV line. At what distance from the wire is the density of the magnetic field equal to the density of the earth's magnetic field B(earth) = 4 × 10^-5 T? What is the force on the L= 200 m long sections of wires between two supporting pillars, if the two wires are spaced d= 5 m?

    2. Relevant equations

    P= V*I
    B= (μ(0)*I)/ (2πr)
    F= I*L*B

    3. The attempt at a solution

    First part: At what distance from the wire is the density of the magnetic field equal to the density of the earth's magnetic field BZ = 4 × 10^-5 T?

    P= V*I → I= P/V
    I= 100 MV/ 220 kV
    I= 454.5 A

    B= (μ(0)*I)/ (2πr) → r= (μ(0)*I)/ (2πB)
    r= (4π x 10-7 N/A²*454.5 A)/ (2π*4 × 10^−5 T)
    r= 2.27 m

    Are my calculations correct?:confused:

    Second part: What is the force on the 200 m long sections of wires between two supporting pillars, if the two wires are spaced 5 m?

    F= I*L*B
    F= I*L*((μ(0)*I)/ (2πd))
    F= 1.65 N

    Are my calculations correct?:confused:

    Thank you for helping!:smile:
     
  2. jcsd
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