An electrical substation has two busbars that are aligned parallel to each other

Question

An electrical substation has two busbars that are aligned parallel to each other and located 0.8 meters apart. At a particular instant, one busbar is carrying 1.9 kA and the other busbar is carrying (0.5)* 1.9 kA in the other direction (i.e., it has a phase offset of 120 degrees). Assuming that the current in the first busbar creates a magnetic field of strength B=? I1 / 2?r Teslas, the air around the busbars has a permeability of ?=?0=4 ?10-7 H/m, and the force per unit length experienced by the second busbar is determined by F=? I1 I2 / 2?r, determine the force per unit length felt by the second busbar in N/m:

An electrical substation has two busbars that are aligned parallel to each other and located 0.8 meters apart. At a particular instant, one busbar is carrying 1.9 kA and the other busbar is carrying (0.5)* 1.9 kA in the other direction (i.e., it has a phase offset of 120 degrees). Assuming that the current in the first busbar creates a magnetic field of strength B=? I1 / 2?r Teslas, the air around the busbars has a permeability of ?=?0=4 ?½10-7 H/m, and the force per unit length experienced by the second busbar is determined by F=? I1 I2 / 2?r, determine the force per unit length felt by the second busbar in N/m:

Explanation / Answer

force between two parallel wires is given by F = u0i1i2L/2pid

where u0 = constnat = 4pi*10^-7 H/m,

i1, i2 are the currents ,

L s the length o the wire,

d is the distqance between these two wires

if current are in same directiion, there exists , they exert attractive force on each other

and if currents are in opposite direction, they exert repulsive force

so here we apply

F/L = 4pie-7 * 1900* 1900*0.5 /(2pi * 0.8)

F/L = 0.4512 N

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