Tru Physics

Magnetic Force

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Tru Physics
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Introduction

The magnetic force is the force exerted between magnetic fields and moving charged particles. When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field. The equation for the magnetic force F_B on a charged particle is given by:

F_B = q(\vec{v} \times \vec{B})

where:

  • q is the charge of the particle,
  • \vec{v} is the velocity of the particle, and
  • \vec{B} is the magnetic field.

Magnetic Force on Current-Carrying Wires

For a straight wire carrying a current I in a magnetic field \vec{B}, the magnetic force \vec{F}_B is given by:

\vec{F}_B = I \vec{L} \times \vec{B}

where \vec{L} is the vector length of the wire in the direction of the current.

Lorentz Force

The total electromagnetic force experienced by a charged particle is known as the Lorentz force. The Lorentz force is the vector sum of the electric force and the magnetic force. The equation for the Lorentz force F is:

\vec{F} = q\vec{E} + q(\vec{v} \times \vec{B})

Ampère’s Force Law

Ampère’s force law describes the force between two current-carrying conductors. The force per unit length (F/L) between two parallel conductors carrying currents I_1 and I_2 separated by a distance r is given by:

\dfrac{F}{L} = \dfrac{\mu_0 I_1 I_2}{2\pi r}

Magnetic Materials

Magnetic materials can be broadly classified as diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic materials based on their magnetic properties. The study of these materials and the forces within them is a large part of magnetism and condensed matter physics.

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