Figure 29-63 shows wire 1 in cross section; the wire is long...

Figure $29-63$ shows wire 1 in cross section; the wire is long and straight, carries a current of 4.00 $\mathrm{mA}$ out of the page, and is at distance $d_{1}=2.40 \mathrm{cm}$ from a surface. Wire $2,$ which is parallel to wire 1 and also long, is at horizontal distance $d_{2}=5.00 \mathrm{cm}$ from wire 1 and carries a current of 6.80 $\mathrm{mA}$ into the page. What is the $x$ component of the magnetic force per unit length on wire 2 due to wire 1$?$

Figure $29-63$ shows wire 1 in cross section; the wire is long and straight, carries a current of 4.00 $\mathrm{mA}$ out of the page, and is
at distance $d_{1}=2.40 \mathrm{cm}$ from a surface. Wire $2,$ which is parallel
to wire 1 and also long, is at horizontal distance $d_{2}=5.00 \mathrm{cm}$ from wire 1 and carries a current of 6.80 $\mathrm{mA}$ into the page. What
is the $x$ component of the magnetic force per unit length on wire
2 due to wire 1$?$

Key Concepts

Magnetic Field of a Long Straight Conductor

This concept refers to the magnetic field generated by a long, straight current-carrying conductor, which can be determined using Ampere’s law. The field at a distance r is given by B = (??I)/(2?r), and this field is crucial for understanding the interactions between currents in nearby wires.

Lorentz Force on a Current-Carrying Conductor

This principle describes the force experienced by a segment of wire carrying current when placed in a magnetic field. The force per unit length is obtained from the cross product F = I(L × B), where the direction of the force follows the right-hand rule. This is key to determining the magnetic force exerted on one wire by the magnetic field produced by another.

Right-Hand Rule

This is a mnemonic tool used to determine the direction of the magnetic field around a current-carrying conductor as well as the direction of the force acting on another current-carrying wire in that magnetic field. It is fundamental for visualizing and solving problems involving current elements and magnetic forces.

Magnetic Interaction Between Parallel Currents

This concept focuses on the attractive or repulsive forces between two parallel wires carrying currents. The interaction arises because each wire produces a magnetic field that exerts a force on the other wire. Understanding this principle is essential when analyzing the net force per unit length between the two wires in the given problem.

Transcript

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