Motion in Combined Electric and Magnetic Field Video Lecture | Physics for JEE Main & Advanced

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ahead with part 11 now let us look at
the motion in combined electric and
magnetic field till now we consider the
presence of magnetic fields alone the
ignored electric field now let us
suppose that if electric field as well
as magnetic field both are present
together in that case how would the
motion of the particle look like now to
look at the combined effect of electric
and magnetic field to keep things simple
as of now we will assume that let us
suppose that the electric field and
magnetic field are perpendicular to each
other and the velocity of the particle
is perpendicular to each of them that
means velocity is perpendicular to
electric field as well as magnetic field
so we can assume it somewhat like this
let us suppose that this is my XY and z
axis so this is my X this is my Y and
this is my z axis so let us suppose that
electric field is along this axis
magnetic field is along this axis and
the velocity of the particle is along
this axis so that means three of them
are mutually perpendicular to each other
under this assumption we will try to see
that how would be the motion of the
particle under the influence of electric
and magnetic field books so what is the
net force that acts on a particle due to
electric as well as magnetic field it
will be pillock F electric plus F
magnetic which will be equal to Q E Plus
Q into V cross B right now in this case
what is your E e is nothing but e I cap
what is V B is nothing but V J cap and
what is B it is nothing but V kpac like
so now in this expression you can write
that the connect force will be equal to
Q e I cap plus Q into V cross V so what
does V cross V let us calculate V cross
B here B cross B let us of course this
is i j k now what is V V is V k cap that
means 0 0 V and V is V J cap so which is
0 B 0 this is how you calculate cross
product right so this will become I 2 0
minus V B right so this will be equal to
minus V B I cap so V cross B will be
equal to minus V B I cap so this is
equal to Q P minus Q V B I cap right so
from here we can write Q into e minus V
B I cap so this is the net force that
will act on the charge particle so the
net force due to electric as well as
magnetic field that will act on the
charge particle will be equal to this
value so the net force will act along
the x axis that means along the
direction of the electric field so you
understood how do we evaluate this now
let us suppose that if we had not
assumed because of our assumption of a
calculation became very simple had me
not as you this in that is you would
have got this cross product in terms of
IG K so you would have got this Force
which acting on the particle in it would
have components along X Y as well as Z
axis right so now you must be thinking
and why did we study this because this
has a very important application which
we will see
smell so from this we conclude that the
electric and magnetic forces act in
opposite direction so if you see from
here what is where is your electric
force this is your electric force which
is acting which is positive now if you
see here what is the magnetic force the
magnetic forces minus u vb right i cap
that means if your electric force is
acting along plus x axis the magnetic
force will be acting along minus x axis
right that is what it says so that means
electric and magnetic forces are in
opposite direction this is the direction
of electric force then this will be the
direction of magnetic force so that was
our conclusion here thank you please
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