光ピンセット
( E ⋅ ∇ ) E = ∇ ( 1 2 E 2 ) − E × ( ∇ × E ) {\displaystyle \left({\boldsymbol {E}}\cdot \nabla \right){\boldsymbol {E}}=\nabla \left({\frac {1}{2}}E^{2}\right)-{\boldsymbol {E}}\times \left(\nabla \times {\boldsymbol {E}}\right)}
∇ × E = − ∂ B ∂ t {\displaystyle \nabla \times {\boldsymbol {E}}=-{\frac {\partial {\boldsymbol {B}}}{\partial t}}}
ベクトル演算、および電磁誘導の法則に従った演算を考慮して式をまとめると
F = α [ 1 2 ∇ E 2 − E × ( ∇ × E ) + d E d t × B ] {\displaystyle {\boldsymbol {F}}=\alpha \left[{\frac {1}{2}}\nabla E^{2}-{\boldsymbol {E}}\times \left(\nabla \times {\boldsymbol {E}}\right)+{\frac {d{\boldsymbol {E}}}{dt}}\times {\boldsymbol {B}}\right]}