Lorentz force equation

 Lorentz Force Equation

 

The force experienced by current element in magnetic field is given as sum of force due to electric field and magnetic field. 

Force due to electric field:

A region is said to be characterized by an electric field if a particle of charge q moving with

a velocity v experiences a force Fe, independent of v. The force, Fe, is given by

             Fe = qE ---------------------------------------- (1.1)



                  E is the electric field intensity. Measured in newtons per coulomb (N/C) or volts per meter.

Where volt is a newton-meter per coulomb. The line integral of E between two

points A and B in an electric field region gives voltage between A and B. It is the work per unit charge done by the field in the movement of the charge from A to B.

Force due to magnetic field:

If a charged particle experiences a force which depends on v, then the region is said

to be characterized by a magnetic field. The force, Fm, is given by

                    F_m=qv * B

where B is the magnetic flux density.

• the units of B are newtons/coulomb meter per second or Volt seconds per square meter.


• more commonly used units are Weber’s per square meter (Wb/m²) or Tesla (T), where a Weber is a volt-second.


• The surface integral of B over a surface S is the magnetic flux (Wb) crossing the surface.


• The magnitude of the force is qvBsinα, where α is the angle between v and B.

then force experienced by current element in magnetic field is given as sum of force due to electric field and magnetic field i.e. F_e+F_m

                  final equation is given as :                  

                                         F = F_e+F_m

                                         F= (qe) + (qv * B) = q (e + (v * B))