Question

Какая сила действует на каждый метр длины воздушных проводов троллейбусной линии,расположенных на расстоянии 52 метра друг от друга,если сила тока в проводах 2000А?

Answer 1

$F = \frac{ \mu_{0}*I^{2} }{2* \pi *R} = \frac{1,3*10^{-6}*4*10^{6}}{2*3,14*52} = 0,016 H = 16 mH$

Answer 2

Calculation of the Force on Each Meter of Trolleybus Line

To calculate the force acting on each meter of the trolleybus line, we need to know the current flowing through the wires and the distance between them. According to the provided information, the current in the wires is 2000A, and the distance between the wires is 52 meters.

The force acting on each meter of the trolleybus line can be calculated using the formula:

Force = Magnetic Field Strength × Current × Length

The magnetic field strength can be calculated using Ampere's Law, which states that the magnetic field around a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

Let's calculate the force on each meter of the trolleybus line step by step:

1. Calculate the magnetic field strength: - The magnetic field strength can be calculated using the formula: Magnetic Field Strength = (μ₀ × Current) / (2π × Distance) - μ₀ is the permeability of free space, which is a constant equal to 4π × 10⁻⁷ T·m/A. - Current is the current flowing through the wires, which is 2000A. - Distance is the distance between the wires, which is 52 meters. - Plugging in the values, we get: Magnetic Field Strength = (4π × 10⁻⁷ T·m/A × 2000A) / (2π × 52m) - Simplifying the equation, we find: Magnetic Field Strength = (8 × 10⁻⁵ T·m) / (52m) - Calculating the value, we get: Magnetic Field Strength ≈ 1.54 × 10⁻⁴ T

2. Calculate the force on each meter of the trolleybus line: - The force can be calculated using the formula: Force = Magnetic Field Strength × Current × Length - Magnetic Field Strength is approximately 1.54 × 10⁻⁴ T. - Current is 2000A. - Length is 1 meter (since we are calculating the force on each meter of the trolleybus line). - Plugging in the values, we get: Force = (1.54 × 10⁻⁴ T) × (2000A) × (1m) - Simplifying the equation, we find: Force ≈ 0.308 N

Therefore, the force acting on each meter of the trolleybus line, located at a distance of 52 meters from each other, with a current of 2000A, is approximately 0.308 Newtons.