“Magnetic force on moving charge and current carrying
conductor : class 12 notes “ will be very beneficial for the students who are
engaged in the preparation of upcoming
board exam and competitive exam.
In Magnetic force on moving charge topic, the following terms will be
illustrated.
Contents :
* Force on moving
charge in uniform magnetic field
* Magnetic force
formula for moving charge in magnetic field
* Force on current
carrying conductor placed in uniform magnetic field
* Right-hand Palm Rule
No. 2
* Fleming's Left-hand
Rule
* Force Between Two Parallel current carrying
Conductors
* Cause of Magnetic
forces experienced by two current carrying conductor
* Magnitude of mutual
force
Magnetic force on moving charge and current carrying conductor | physics notes class 12
Force on moving charge in uniform magnetic field
* When a charged particle enter in uniform magnetic field with
velocity v , then it experiences a force in direction perpendicular to
plane containing v and B vectors.
* Since force is always perpendicular to velocity, so speed of
charge remains constant in magnetic
field.
Magnetic force formula for moving charge in magnetic field :
* Consider a positive charge +q is moving in a uniform magnetic field B
with a velocity v .
* Let the angle between v and B vector be θ.
* The magnitude F of this force depends on the following
factors :
(i) F ∝ q
(ii) F ∝ v
(iii) F ∝ B
(iv) F ∝ sinθ
Combining relationship
We get , F ∝ qvB sinθ
F = qvB sinθ
( proportionality constant is 1 )
Magnetic Force in Vector form
F = q (V X B
)
* Direction of force is perpendicular to plane containing v
and B vectors.
Force depend on angle :
Case 1: if charge is at rest
in magnetic field
Then , v = 0
So, F = 0
i.e. A
stationary charge experience no force in magnetic field
Case 2 : If θ =00
or θ = 1800
Then , sinθ = 0
So, F = 0
i.e. A charge
moving parallel to magnetic field line experience no force. So it continue to
move with same speed parallel to field .
Case 3 : If θ =900
Then , sinθ = 1
So , Force will
be maximum for this angle , Fm
= qvB
This maximum force rotate charge in
circular path with constant speed. Plane of circular path is perpendicular to
field.
Force on current carrying conductor placed in uniform magnetic field
A current carrying conductor placed in a magnetic
field experiences a force.
* When a current carrying conductor is placed in a uniform
magnetic field, each free electron experiences a force in same direction .
* Since the free electrons are constrained in the conductor,
the conductor itself experiences a force in that direction.
* Thus, Conductor experiences a force in a direction
perpendicular to both, the direction of current and the magnetic field.
Explanation :
* A wire is tied loose between N and S poles of a horse- shoe
magnet. The length of the wire is kept perpendicular to the direction of the magnetic
field between the poles. When an electric current is passed through the wire,
the wire is lifted upwards. This shows that an upward force is acting on the
current-carrying wire.
* On reversing the direction of current, the wire moves
downwards, showing that now the force is acting downwards.
Direction of force :
The direction of the force acting on a
current-carrying conductor in a magnetic field can be found by any of the
following two rules:
(i) Right-hand Palm Rule No. 2:
* If we stretch our
right-hand palm such that the thumb points in the direction the current, the
stretched fingers in the direction of the magnetic field B, then the force on
the conductor will be perpendicular to the palm in the direction of the
palm-front.
(ii) Fleming's Left-hand Rule :
* If the fore-finger, the middle-finger and the thumb of
the left hand are stretched mutually at right angles to one another such that
the fore-finger points in the direction of the magnetic field B and the middle
finger in the direction of the current, then the thumb will point in the
direction of the force F on the conductor.
Expression for force
* Consider a conductor of length L and area of cross-section A
placed at an angle θ to the direction of a uniform
magnetic field B .
* Let
I = current in the conductor
Vd =
drift velocity of free electrons
n = electron density in the conductor
e = charge on each electron
* Force on each electron,
Fe = -e ( vd x B )
Or, Fe
= e ( B x vd )
* Let, Number of free
electrons in per unit volume = n
* Then , total number of free electrons in volume V = nV =
nAL
* Force experienced by conductor of length L ,
F = nAL e ( B x vd )
So, F = nALeBvd sinθ
( Where ,
θ = angle between B and
length of conductor )
F = neA vd B L sinθ
Thus, F =
I LB sinθ ( I = neA vd )
Force in vector form,
F= I ( L X B )
* Direction of force is perpendicular to plane containing L
and B
* length vector is taken in direction of current
Force
Between Two Parallel current carrying Conductors
When
two current carrying parallel conductors are kept at some distance, then they
exert equal and opposite force on each other.
* Force may be attractive or repulsive.
it depend on nature of current in both conductors .
(i)
Like
current ( same direction ) carrying
conductors attract each other
(ii)
Unlike current ( opposite direction
) carrying conductors repel each other
Cause of Magnetic forces experienced by two current carrying conductor
* A current carrying conductor has tendency to move from
strong magnetic field to weak magnetic field.
* Due to this reason , two current carrying conductors exert
force on each other.
(i) If Currents in the same direction
* Both conductors will
set up its own magnetic field.
* In the space between A and B, the two fields are in
opposition and hence they tend to cancel each other. So, magnetic field is
weaken between A and B.
* In the space outside A and B, the two fields assist each
other. So magnetic field increases outside A and B.
* Magnetic lines of force behave as stretched elastic cords.
(ii) Currents in opposite direction
* In the space outside A and B, the two fields are in
opposition and hence they tend to cancel each other. So magnetic field is
reduced .
* In the space between A and B, the two fields assist each
other. So magnetic field is increased.
* So, conductors tend to move toward weaker magnetic field
from the relatively strong magnetic field . Thus they repel each other .
MAGNITUDE OF MUTUAL FORCE
Consider two parallel conductors placed in air and
carrying current i1 and i2
.
Let
I1 = current in conductor A
I2=
current in conductor B
r = distance between conductors
* Magnetic Field produced by conductor A at distance r
Conductor 'B' experiences Magnetic force in presence of magnetic field B1 ,
So , Magnetic force experienced by conductor 'B' of
length L
* Magnetic force on per unit length of conductor = F /L
* Conductor A also experiences equal and opposite force .
Thus in system of two current carrying conductor , Mutual force per unit length of conductor is
Define 1 A
* Mutual force between two current carrying parallel
conductors in per unit length is given
as ,
If i1
= 1 A , i2 = 1 A ,
and r= 1 m
Then , F/L
= 2 x 10-7 x 1x1
/ 1
i.e ,
F/L = 2 x 10-7 N
* Thus, If two parallel
long conductors having equal amount of current are kept at 1 meter distance and
mutual force between them is 2 x 10-7 N ,
then current flowing in each conductor
will be 1 A .
Force between two parallel moving charge
If two charged particle move on parallel straight path
then they exert equal and opposite force to each other .
Let
q1
= Charge of first particle
q2
= charge of second particle
r = distance between parallel path
v1 = speed of charge q1
v2 =
speed of charge q2
Then mutual magnetic force is,
* Like charge exert attractive magnetic force .
* Unlike charge exert repulsive magnetic force.
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