In Fig. 29-64, five long parallel wires in an x y plane are...

In Fig. $29-64,$ five long parallel wires in an $x y$ plane are separated by distance $d=50.0 \mathrm{cm} .$ The currents into the page are $i_{1}=2.00 \mathrm{A}, \quad i_{3}=0.250 \mathrm{A}, \quad i_{4}=4.00 \mathrm{A},$ and $\quad i_{5}=2.00 \mathrm{A}$ the current out of the page is $i_{2}=4.00 \mathrm{A}$ . What is the magnitude of the net force per unit length acting on wire 3 due to the currents in the other wires?

In Fig. $29-64,$ five long parallel wires in an $x y$ plane are separated by distance $d=50.0 \mathrm{cm} .$ The currents into the page
are $i_{1}=2.00 \mathrm{A}, \quad i_{3}=0.250 \mathrm{A}, \quad i_{4}=4.00 \mathrm{A},$ and $\quad i_{5}=2.00 \mathrm{A}$
the current out of the page is $i_{2}=4.00 \mathrm{A}$ . What is the magnitude of the net force per unit length acting on wire 3 due to the currents in the other wires?

Key Concepts

Magnetic Field of a Long Straight Conductor

A long straight current-carrying wire produces a magnetic field that circulates around the wire. According to Ampere’s law (or equivalently the Biot–Savart law), the magnitude of the magnetic field at a distance r from the wire is given by B = ??i/(2?r), where ?? is the permeability of free space. This magnetic field forms concentric circles around the wire and is a fundamental concept for understanding magnetic interactions between currents.

Magnetic Force on a Current-Carrying Conductor

When a current-carrying conductor is placed in a magnetic field, it experiences a force described by the Lorentz force law. The force per unit length on the conductor is given by F/L = iB sin?, where i is the current, B is the magnetic field strength, and ? is the angle between the direction of current and the magnetic field. This principle explains phenomena such as the attraction or repulsion between parallel currents and is central to many electromagnetic devices.

Superposition Principle in Magnetism

The superposition principle states that the net magnetic field created by several sources is the vector sum of the individual fields produced by each source. This principle is essential when calculating the resultant magnetic field at a point due to multiple current-carrying wires, allowing for the analysis of complex magnetic interactions by adding the contributions from each wire.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field around a current-carrying conductor and the direction of the force on a conductor in a magnetic field. By aligning the thumb in the direction of the current, the curled fingers indicate the circular direction of the magnetic field lines. This rule is crucial for visualizing and predicting the outcomes of magnetic interactions in various electromagnetic scenarios.

Please give Ace some feedback