ローレンツ力
電場 E ( t , x ) {\displaystyle {\boldsymbol {E}}(t,{\boldsymbol {x}})} と磁束密度(磁場) B ( t , x ) {\displaystyle {\boldsymbol {B}}(t,{\boldsymbol {x}})} の空間中を運動する荷電粒子(位置 r ( t ) {\displaystyle {\boldsymbol {r}}(t)} 、速度 v ( t ) {\displaystyle {\boldsymbol {v}}(t)} 、電荷 q {\displaystyle q} )に作用する電磁気的な力 F ( t ) {\displaystyle {\boldsymbol {F}}(t)} は
F ( t ) = q E ( t , r ( t ) ) + q v × B ( t , r ( t ) ) = q { E ( t , r ( t ) ) + v × B ( t , r ( t ) ) } {\displaystyle {\boldsymbol {F}}(t)=q{\boldsymbol {E}}(t,{\boldsymbol {r}}(t))+q{\boldsymbol {v}}\times {\boldsymbol {B}}(t,{\boldsymbol {r}}(t))=q{\big \{}{\boldsymbol {E}}(t,{\boldsymbol {r}}(t))+{\boldsymbol {v}}\times {\boldsymbol {B}}(t,{\boldsymbol {r}}(t)){\big \}}}