What is the magnitude of magnetic force per unit length on a...

What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of $30^{\circ}$ with the direction of a uniform magnetic field of $0.15 \mathrm{~T}$ ?

Key Concepts

Magnetic Force per Unit Length

This concept refers to the force acting on a unit length of a current-carrying wire in a magnetic field. It is derived from the basic force equation by considering the force distributed along the length of the wire. This measurement is particularly useful for analyzing systems where the total length of the conductor in the field is either unspecified or variable, making it easier to compare the force effects independently of the wire's length.

Magnetic Field

A magnetic field is a vector field that represents the distribution of magnetic force in space, usually measured in teslas (T). It influences moving charges and magnetic dipoles, and is a fundamental aspect of magnetism. In this context, it provides the environment in which the current-carrying conductor experiences a force.

Magnetic Force on a Current-Carrying Conductor

This concept is based on the Lorentz force law, which states that a current-carrying conductor in a magnetic field experiences a force. The force magnitude is proportional to the current, the strength of the magnetic field, the length of the conductor within the field, and the sine of the angle between the current direction and the magnetic field. It captures how electric currents interact with magnetic fields to produce mechanical effects.

Angle Dependence of Magnetic Force

The magnetic force on a current-carrying conductor depends on the sine of the angle between the direction of the current and the magnetic field. This means that the force is maximized when the current is perpendicular to the field (sin 90° = 1) and is zero when the current is parallel to the field (sin 0° = 0). This angular dependence is crucial in determining how much of the effective field strength contributes to the force.

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