91Ó°ÊÓ

To understand the magnetic forces between parallel conductors, we begin with calculating the magnetic field. A long, straight wire carrying a current generates a magnetic field around it. The magnitude of this field at a distance \( r \) from the wire can be calculated using the formula: \[ B = \frac{\mu_0 I}{2 \pi r} \] where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space \(( 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A})\), \( I \) is the current flowing through the wire, and \( r \) is the distance from the wire.

For example, if you have a wire carrying a current of 25 A, situated 0.35 meters from the point of interest, the magnetic field there, \( B_1 \), would be approximately \( 1.43 \times 10^{-5} \, \text{T} \). This calculation forms the basis for understanding the forces between wires.

When wires carry an electric current, they create a magnetic field around them. This principle is crucial in determining how they affect each other. Each wire not only generates its magnetic field but also influences nearby current-carrying conductors. The strength of the magnetic field depends on the amount of current and the distance from the wire, as discussed earlier.

Current-carrying wires are used in numerous applications such as power transmission and electromagnetic devices because of their unique ability to generate magnetic fields, which is central to many electromagnetic systems.

In this case, the transmission lines carry 25 A and 75 A, showing a significant potential to influence each other through their respective fields. Their interaction depends on both the magnitude and the direction of the currents they carry.

The electromagnetic force between two parallel current-carrying conductors can be understood using the formula: \[ F = I L B \] where \( F \) is the force, \( I \) is the current in the second wire, \( L \) is the length of the wire segment, and \( B \) is the magnetic field due to the first wire.

When the field from one wire interacts with the other, a force is exerted on the latter. For a wire of length 15 m segment carrying 75 A current, in the magnetic field \( B_1 \) produced by the first wire carrying 25 A, calculation shows the exerted force \( F_1 \) to be approximately \( 1.61 \times 10^{-1} \, \text{N} \). This force reflects the powerful interaction stemming from their respective magnetic fields.

The magnitude of the force is determined by the product of the current, length, and magnetic field, showing how all these elements interact to produce measurable forces.

When two parallel wires carry current in the same direction, attractive forces develop between them. These forces arise due to the interaction of the magnetic fields they generate. According to the right-hand rule, parallel currents attract each other, which is a fundamental aspect of electromagnetic force interactions.

In the given exercise, the two high-current transmission lines carry currents in the same direction. The forces calculated for each wire using their respective magnetic fields and currents were both approximately \( 1.61 \times 10^{-1} \, \text{N} \). Because the currents are parallel, the nature of the force is attractive.

Understanding these forces is essential in designing systems like power lines and circuits, ensuring they function correctly without unwanted repulsion or attraction, thereby maintaining stability in the system.