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

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

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the resultant vector from a cross product. When applied to the calculation of magnetic forces, it tells you the direction of the force on a current-carrying wire: pointing your thumb in the direction of the current and your fingers in the direction of the magnetic field, your palm then indicates the direction of the force.

Vector Cross Product

The vector cross product is a mathematical operation used to determine a vector that is perpendicular to two given vectors. In the context of magnetic force, it is used to compute the direction of the force on a current-carrying wire by taking the cross product of the wire’s length vector and the magnetic field vector.

Lorentz Force Law

The Lorentz force law states that a moving electric charge in a magnetic field experiences a force perpendicular to both its velocity and the magnetic field. For a current-carrying wire, this results in a net force on the wire, which is determined by summing the forces on the moving charges within the conductor.

Magnetic Force on a Current-Carrying Conductor

This concept explains that a current-carrying wire placed within a magnetic field experiences a force. The force is given by the equation F = I (L x B), where I is the current, L is the vector representing the length and orientation of the wire, and B is the magnetic field. This relationship is fundamental in understanding how electric currents interact with magnetic fields.