Figure 29-82 shows, in cross section, two long parallel...

Figure $29-82$ shows, in cross section, two long parallel wires spaced by distance $d=10.0 \mathrm{cm}$ ; each carries 100 $\mathrm{A}$ , out of the page in wire $1 .$ Point $P$ is on a perpendicular bisector of the line connecting the wires. In unit-vector notation, what is the net magnetic field at $P$ if the current in wire 2 is (a) out of the page and (b) into the page?

Figure $29-82$ shows, in cross section, two long parallel wires spaced by distance $d=10.0 \mathrm{cm}$ ; each carries 100 $\mathrm{A}$ , out of the
page in wire $1 .$ Point $P$ is on a perpendicular bisector of the line connecting the wires. In unit-vector notation, what is the net magnetic
field at $P$ if the current in wire 2 is (a) out of the page and (b) into the
page?

Key Concepts

Magnetic Field from a Long Straight Conductor

A long, straight current-carrying conductor produces a magnetic field whose magnitude at a distance r from the wire is given by B = (??I)/(2?r), where ?? is the permeability of free space and I is the current. This principle is key for determining the individual magnetic fields produced by each wire at a given point.

Right-Hand Rule

The right-hand rule is used to determine the direction of the magnetic field created by a current-carrying wire. By pointing the thumb of the right hand in the direction of the conventional current, the curl of the fingers shows the direction of the magnetic field lines. This rule is essential for understanding how the direction of the current (into or out of the page) influences the magnetic field's orientation.

Superposition Principle

The superposition principle for magnetic fields states that when multiple magnetic fields are present, the net magnetic field at any point is the vector sum of the individual fields. This concept is particularly important when evaluating the combined effect of the magnetic fields produced by two or more wires at a specific location.

Unit Vector Notation

Unit vector notation is a method to express vector quantities by breaking them down into components along the coordinate axes, typically using i, j, and k for the x, y, and z directions respectively. This notation allows for a clear representation of both the magnitude and direction of the magnetic field, facilitating the process of vector addition when multiple fields are involved.

Transcript

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