Unni Namboodiri has written:

'Equivariant vector fields on spheres'

name as many scalar fields and vector fields as u can?

U. Koschorke has written:

'Differential Topology' -- subject(s): Congresses, Differential topology

'Vector fields and other vector bundle morphisms' -- subject(s): Singularities (Mathematics), Vector bundles, Vector fields

Electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.

Both, E=Es + Ev = cB therefore, B= Es/c + Ev/c = Bs + Bv.

The electric and magnetic fields are quaternion fields consisting of a scalar field and a vector field.

Contemporary Physics has not realized this yet. Correct Relativity Theory is a manifestation of quaternion fields, consisting of a scalar field and three vector fields. This shows up in the Energy Momentum four vector, E= Es +cmV.

Actually the Lorentz Force is both scalar and vector: F=qvB = - qv.B + qvxB

it makes no sense consider only qvxB and to ignore qv.B.