A 1.0 -m-long segment of wire lies along the x -axis and...

A 1.0 -m-long segment of wire lies along the $x$ -axis and carries a current of $2.0 \mathrm{A}$ in the positive $x$ -direction. Around the wire is the magnetic field of $(3.0 \hat{\mathbf{i}} \times 4.0 \hat{\mathbf{k}}) \times 10^{-3} \mathrm{T}$. Find the magnetic force on this segment.

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept involves determining the force experienced by a wire carrying an electric current when placed in an external magnetic field. The fundamental equation for this phenomenon is F = I (L × B), where F is the force, I is the current, L is the vector representing the length and direction of the wire, and B is the magnetic field. This principle is central in electromagnetism and is the basis for the operation of many electrical devices such as motors and generators.

Vector Cross Product

The vector cross product is a mathematical operation that takes two vectors and produces a third vector which is perpendicular to the plane containing the original vectors. In the context of magnetic forces, the cross product determines both the magnitude and the direction of the force acting on a current element in a magnetic field. The right-hand rule is often used to determine the direction of the resultant vector, making this concept essential for understanding how forces in magnetic fields are oriented.

Magnetic Field

A magnetic field is a vector field that represents the magnetic influence on moving electric charges, electric currents, and magnetic materials. It is characterized by both magnitude and direction and arises from the motion of electrically charged particles. The magnetic field interacts with current-carrying conductors to produce a force, as described by the Lorentz force law, making it a key component in the study of electromagnetism.

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