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Mathematical Physics

Magnetism Fundamentals

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Magnetic Flux

\Phi = \int \mathbf{B} \cdot d\mathbf{A}

, where

\Phi

represents the magnetic flux,

\mathbf{B}

is the magnetic field, and

d\mathbf{A}

is an infinitesimal area vector orthogonal to the field.

Electromagnetism

The branch of physics that studies the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

Lorentz Force

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

, where

\mathbf{F}

is the force,

q

is the charge,

\mathbf{E}

is the electric field,

\mathbf{v}

is the velocity of the charge, and

\mathbf{B}

is the magnetic field.

Ferromagnetism

A physical phenomenon by which certain materials can exhibit a lasting magnetization.

Magnetic Field

A vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

Magnetic Moment

\mathbf{\mu} = I \cdot \mathbf{A}

, where

\mathbf{\mu}

is the magnetic moment,

I

is the current, and

\mathbf{A}

is the area vector of the loop.

Paramagnetism

A form of magnetism which occurs only in the presence of an externally applied magnetic field.

Diamagnetism

A very weak form of magnetism that is induced by a change in the orbital motion of electrons due to an applied magnetic field.

Ampere's Circuital Law

\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0\left(I_\text{enc} + \epsilon_0\frac{d\Phi_E}{dt}\right)

, where the integral is the line integral over a closed loop,

\mathbf{B}

is the magnetic field,

d\mathbf{l}

is the differential element of length,

\mu_0

is the vacuum permeability,

I_\text{enc}

is the current enclosed by the loop, and

\frac{d\Phi_E}{dt}

is the rate of change of electric flux.

Magnetic Permeability

\mu = \frac{B}{H}

, where

\mu

is the magnetic permeability,

B

is the magnetic flux density, and

H

is the magnetic field strength.

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