One long wire lies along an x Figure 29-59 Problem 54 . axis...

One long wire lies along an $x$ Figure 29-59 Problem $54 .$ axis and carries a current of $60 \mathrm{~A}$ in the positive $x$ direction. A second long wire is perpendicular to the $x y$ plane, passes through the point $(0,4.0 \mathrm{~m}, 0)$, and carries a current of $40 \mathrm{~A}$ in the positive $z$ direction. What is the magnitude of the resulting magnetic field at (a) the point $(0,2.0 \mathrm{~m}, 0)$ and (b) the point $(2.0 \mathrm{~m}, 4.0 \mathrm{~m}, 0)$ ?

One long wire lies along an $x$
Figure 29-59 Problem $54 .$ axis and carries a current of $60 \mathrm{~A}$ in
the positive $x$ direction. A second long wire is perpendicular to the $x y$ plane, passes through the point $(0,4.0 \mathrm{~m}, 0)$, and carries a current of $40 \mathrm{~A}$ in the positive $z$ direction. What is the magnitude of the resulting magnetic field at (a) the point $(0,2.0 \mathrm{~m}, 0)$ and (b) the point $(2.0 \mathrm{~m}, 4.0 \mathrm{~m}, 0)$ ?

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Key Concepts

Magnetic Field from a Long Straight Current

This concept involves the magnetic field produced by a long, straight conductor carrying an electric current. Using Ampère’s Law, the magnetic field at a distance r from the wire is given by B = (?0 * I) / (2? * r). The field lines form concentric circles around the wire, and this formula is fundamental in calculating the strength of the field at various points away from the wire.

Right-Hand Rule

The right-hand rule is a guide used to determine the direction of the magnetic field around a current-carrying conductor. By aligning the thumb of the right hand with the direction of the current, the curled fingers indicate the circular direction of the magnetic field lines. This rule is essential for understanding the orientation of magnetic fields in three-dimensional space.

Superposition Principle

The superposition principle states that when multiple independent sources produce magnetic fields, the resultant magnetic field at any given point is the vector sum of the individual fields. This principle is critical when analyzing systems with multiple currents, as it allows for the computation of the net magnetic field by considering the contribution of each conductor individually.

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