Question

«два параллельных прямолинейных проводника находятся в вакууме.определите расстояние между проводниками если в следствии их взаимодействия на отрезок проводника длиной 50 см действует сила 2мН при токах в проводниках 100 и 40А.».

Answer 1

F = (μ*μ₀*I₁*I₂*L)/(2*π*d)
где:
μ - магнитная проницаемость среды ( в вакууме 1)
μ₀ - магнитная постоянная
I₁;I₂ - силы тока в проводниках
L - длинна проводников
d - расстояние между проводниками 

2*10^-3 = (1*4*π*10^-7*100*40*0.5)/(2*π*d)

d = 0.2 метра

Answer 2

Calculation of the Distance Between Parallel Conductors

To determine the distance between two parallel straight conductors in a vacuum, we can use the formula for the force between two parallel conductors:

F = (μ₀ * I₁ * I₂ * L) / (2π * d)

Where: - F is the force between the conductors - μ₀ is the permeability of free space (4π * 10^-7 T·m/A) - I₁ and I₂ are the currents in the conductors - L is the length of the conductor segment where the force is acting - d is the distance between the conductors

Given that the force acting on a 50 cm conductor segment is 2 mN (0.002 N), with currents of 100 A and 40 A in the conductors, we can rearrange the formula to solve for d:

d = (μ₀ * I₁ * I₂ * L) / (2π * F)

Substituting the given values:

d = (4π * 10^-7 T·m/A * 100 A * 40 A * 0.5 m) / (2π * 0.002 N)

Simplifying the equation:

d = (8 * 10^-5 T·m * 0.5 m) / 0.002 N

d = 0.02 m

Therefore, the distance between the parallel conductors is 0.02 meters or 2 centimeters.