
PHYSICS12
Chapter 14  Magnetic effect of electric current
Definations:
1. Magnetic field: The space or region around the magnet in which magnetic influence
can be experienced.
2. Magnetic field intensity: The magnetic field intensity at a point inside the magnetic is the
magnetic force per unit pole strength of north pole. i.e. B= F/m where, F= magnetic strength
m= pole strength Unit of pole strength (m)= Ampere meter (Am)
Unit of B = N/Am Tesla (T) in SI Gauss in CGS [1T = 10^{4} Gauss] The
direction of the magnetic field intensity is away from north and towards south pole. 3.
Magnetic lines of force: The imaginary lines which represents the magnetic field. The path
followed by north pole of compass needle when it is free to move as shown in figure:
4. Magnetic
flux: The magnetic flux associated with the surface is the number of magnetic lines of force
passes through that surface.
5.
Magnetic flux density: The flux density at a point inside a magnetic field is the magnetic flux
passing normally through unit surface area. i.e. B= /A = weber/m^{2} Tesla (T)
therefore, = BA, when magnetic lines of force passes normally.
When the magnetic lines of force are not
passes normally but makes an angle θ with the normal then magnetic flux is given by: Φ= AB
cosθ
Force on moving charge in uniform magnetic field
Consider a '+q' charge is moving in a uniform magnetic field B, with velocity V, making an angle θ
with the direction of magnetic field. Then the charge particle experiences the force known as
magnetic lorentz force along zaxis (i.e. perpendicular to
the plane of
and
). Experimentally it is found that the force is:
1.
Directly proportional to
magnetic field. i.e. F_{m} ∝ B 2.
F_{m} ∝ q 3. F_{m} ∝ v 4.
F_{m} ∝ sinθ
Combining all these equations we get, F
_{m} ∝ Bqv sinθ F
_{m}= kBqv sinθ where 'k' is proportionality constant and its value is found to be 1.
therefore, F
_{m}= Bqv sinθ In vector form,
= q (
x
) i.e.
is perpendicular to
and
Special Cases:
1. If V=0, F_{m}=0
i.e. the charge particle at rest doesn't experienced force.
2. If θ= 0^{o}, 180^{o} F
_{m}= 0 i.e. when the velocity of charge particle is parallel or antiparallel to the
direction of magnetic field, then it doesn't experience force and no acceleration is produced in
the charged particle and therefore speed of charge particle is uniform and hence kinetic energy
remains constant. No work is done by this force in the charge particle. Hence the path followed by
the charged particle is straight line.
3. If θ= 90
_{o}, F_{m}= Bqv (maximum) When the velocity is perpendicular to the direction
of magnetic field, then charge particle experiences maximum force. According to Fleming's left
hand rule, F
_{m} perpendicular to v, then this force allowed to move the charge particle in a circular
path and speed remains uniform and therefore kinetic energy remains constant. No work is done by
this force on the charge particle as, W= F_{s} cos90
_{o} therefore, W= 0
4. When the velocity of charge particle is neither
parallel, antiparallel nor perpendicular but makes and angle θ with the direction of magnetic
field.
Then the path followed by the charge is spiral/helical.
Torque on current carrying rectangular coil in uniform magnetic field.
Consider a rectangular coil PQRS is placed in a uniform magnetic field B. The four sides of the
rectangule can be supposed to be four current carrying straight conductor. Here the sides PQ and RS
is perpendicular to the direction of magnetic field whereas
the sides QR and SP makes an angle θ with the direction of magnetic field. Let, length of
rectangle = PQ = RS = l and
breadth of rectangle = QR = SP = b The force experiences by the conductor PQ and RS is
given by, F
_{1}= BIl F
_{3}= BIl Similarly, the force experiences by the conductor QR and SP is given by,
F
_{2}= BIb sinθ F
_{3}= BIb sinθ The direction of this forces is given by fleming's left hand rule.
The forces F_{2} and F_{4} are equal and opposite and have same line of action.
So, they together cannot constitute a couple to produce torque.
On the other hand, the forces F_{1} and F
_{3} are equal and opposite and have different line of action. So, they together can
constitute a couple to produce torque in the coil. Therefore the torque due to couple is given by,
𝞃 = Either force x perpendicular distance between the forces = F
_{1} or F_{3} XYT
𝞃 = F
_{1} or F_{3} x b cosθ BIl x bcosθ 𝞃 = BIA cosθ if the coil is N
time turns, 𝞃 = BINA cosθ
Special Cases: 1. If θ= 0
^{o}, 𝞃= BINA (maximum) 2. If θ= 90^{o}, 𝞃= 0 (no torque)
Hall effect:
When current is passed through a conductor along xaxis
and the conductor is placed in a uniform magnetic field
along yaxis then the potential difference p.d. is
produced in between the conductor such that electric
field is produced in between the conductor
along zaxis. This effect is known as Halleffect. The
p.d. produced is call Hall voltage and the field is
called Hall field. Let 'I' be the current through
the conductor along xaxis and the conductor having
breadth 'b' and thickness 't' is placed in a uniform
magnetic field 'B' along yaxis. Let, v_{d} be
the drift velocity of the electrons then the magnetic
force on each electron is given by,
F
_{m}= Bev
< (i) (along zaxis in the upward direction)
Due to this force, the electrons inside the conductor tends to move in the upward
direction leaving excess +ve charge at the lower surface and excess negative charge at the
upper surface.
Due to this separation of charges, p.d. is produced inside the conductor. As a result,
electric field is produced inside the conductor along zaxis.
The flow of electrons in the upward direction will continue until the magnetic force on
the electron must be balances by electric force on the electron (downward direction). Let
'E'
be the strength of electric field then electric force on each electron is given by,
F
_{e}= eE
< (ii)
At equilibrium, F
_{m} = F_{e} Bev = eE v= E/B
< (iii)
The current flowing through the conductor is given by, I= venA I= (E/B)en
bt I= (v_{H}/b.B) enbt v
_{H}= (IB)/(ent) Now, current density is given by J= I/A
J= (venA)/A
J= ven J= (E/B)en 1/ne = E/JB = R
_{H}= Hall coefficient
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