# Magnetic field and magnetic force between wires

1. Jan 14, 2010

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?

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?

Thank you for helping!