A wire carries a steady current of 2.40 A. A straight...

A wire carries a steady current of $2.40 \mathrm{~A}$. A straight section of the wire is $0.750 \mathrm{~m}$ long and lies along the $x$ axis within a uniform magnetic field of magnitude $B=1.60 \mathrm{~T}$ in the positive $z$ direction. If the current is in the $+x$ direction, what is the magnetic force on the section of wire?

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic device used to determine the direction of the vector resulting from a cross product. In the context of magnetic forces, it helps in visualizing the direction of the magnetic force acting on the wire, indicating that the force is perpendicular to both the direction of the current and the magnetic field.

Cross Product

The cross product is a mathematical operation used in vector analysis that determines a vector perpendicular to two given vectors. It is essential in calculating the magnetic force on a current-carrying wire, as the force vector is given by the cross product of the wire’s length vector and the magnetic field vector.

Uniform Magnetic Field

A uniform magnetic field is one in which the magnetic field strength and direction remain constant throughout the region of interest. This concept is important because it simplifies the calculation of forces on a current-carrying conductor by ensuring that the magnetic field interacts with the conductor in a consistent manner along its length.

Magnetic Force on a Current-Carrying Wire

This concept involves understanding that a wire carrying an electric current experiences a force when placed in a magnetic field, due to the interaction between the current and the field. The force is described by the equation F = I (L x B), where I is the current, L is the length vector of the wire, and B is the magnetic field.

Lorentz Force Law

The Lorentz force law is a fundamental principle in electromagnetism which states that a charged particle moving in a magnetic field experiences a force perpendicular to both its velocity and the magnetic field. For a current-carrying conductor, this law is applied in the form of the magnetic force on a current element, summarizing the cumulative effect of the force on moving charges within the wire.

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