let us discuss about electromagnetic force
on a moving charge in external fields. about
this we can write. when. a charge q. moving
at, velocity. v vector. enters in a region
of. magnetic field. with magnetic induction
b vector. it experiences. a force, given as.
this is force which is given as force vector
is written as q multiplied by v cross b. this
is the expression for magnetic force it is
our equation number 1. which gives the, magnetic
force experience by a charge particle this
is, a direct expression you need to. grasp.
because right now we are not going into how
the expression is coming. this was obtained
by laurentz force equation. and we can say.
if in space. an electric field e vector also
exist. total electro magnetic force. on the
particle. will be given as. this written as
f which is written as f electromagnetic this
is total electromagnetic force which is written
as q-e vector. which is the electric component
of the force plus, the magnetic force is q
v cross b vector. this is the equation 2.
and here we can write this equation 2 is called.
laurentz force equation. which gives. total
electromagnetic force. on a particle. which
is constant. when observed. from all. inertial
reference frames. many students might feel
that as the force vector depends on velocity
vector this must be a frame dependent parameter
but it is not. this force remain constant
whenever it is observed from any kind of inertial
reference frame because. even if the 
frame is moving, this velocity vector changes
but when observed from moving reference frame.
corresponding value of e vector and b vector
may also change due to induction. so net electromagnetic
force follows newton’s law the motion it
remain constant in all inertial reference
frames. however you can say that the magnetic
force q v cross b. which is given by equation
1 is a frame dependant force. which may change
but correspondingly electric force q-e vector
will also change. so net sum of both the forces
that is total electromagnetic force remains
constant but, individual components electric
component and magnetic component of the force
may change. when observed from different kind
of reference frames.
