The Lorentz Force Law and the Field Concept of Electromagnetics

Vocabulary flashcards covering key terms and concepts from the Lorentz force law and the field concept discussion.

Lorentz force law

The total electromagnetic force on a point test charge Q is $F = Q(E + u \times B)$, where E is the electric field, B is the magnetic flux density, and u is the charge’s velocity; valid for time-varying sources.

Field theory

An interpretation where electromagnetic sources emit fields that fill space, so interactions are described by fields rather than action-at-a-distance.

Electric field intensity

A field quantity representing force per unit charge; measured in N/C or V/m; $E = F/Q$ in the limit $Q \to 0$ for a stationary test charge.

Magnetic flux density

A field quantity representing the magnetic influence on moving charges; measured in tesla (T) or Wb/m$^2$; related by $F_m = Q u \times B$.

Electric force

$F_e = Q E$; depends only on the charge magnitude and the electric field; independent of velocity; can do work on a charge.

Magnetic force

$F_m = Q u \times B$; depends on velocity and is perpendicular to both u and B; cannot do work since it acts perpendicular to velocity.

Test charge

A small charge used to measure electric and magnetic fields without disturbing sources; ideally $Q \to 0$.

Test current

A small current used to analyze magnetic effects; the magnetic force on a current element is $dF_m = I d\ell \times B$.

Field quantity

A physical quantity that exists at every point in space and can be measured remotely, as in the field analogy (e.g., odor field).

Field theory analogy (popcorn-odor field)

A didactic example showing a field quantity (odor density) extends through space and can be sensed remotely, not requiring knowledge of the source’s exact position.

Faraday

Proposed the field theory of electromagnetics in the 1830s, introducing E and B as field entities (photons later identified as quanta).

Action-at-a-distance

The idea that forces act instantly at a distance; field theory replaces this with field-mediated interactions.

Electric field units

E is measured in newtons per coulomb (N/C) or volts per meter (V/m).

Magnetic-field units

B is measured in tesla (T), equivalently webers per square meter (Wb/m$^2$); $1 T = 1 N\cdot s/(C\cdot m)$.

Work by electric force

Only the electric force $F_e$ can do work on a charge and change its kinetic energy; the magnetic force does no work.

Velocity dependence of magnetic force

The magnetic force is present only when the charge moves ($u \ne 0$) and is perpendicular to both velocity u and B.

Lab frame definition

E and B are defined as measured in the laboratory reference frame; frame dependence is discussed in later chapters.

Electric Field Intensity Equation

The electric field intensity E is defined as the force per unit charge: $E = F/Q$.

Electric Force Equation

The electric force $F<em>e$ on a charge Q in an electric field E is: $F</em>e = Q E$.

Magnetic Force Equation

The magnetic force $F<em>m$ on a charge Q moving with velocity u in a magnetic field B is: $F</em>m = Q u \times B$.

Magnetic Force on a Current Element

The magnetic force $dF<em>m$ on a current element $I d\ell$ in a magnetic field B is: $dF</em>m = I d\ell \times B$.