Magnetic Field and Magnetic Force
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Transcript Magnetic Field and Magnetic Force
Physics Lecture Resources
Prof. Mineesh Gulati
Head-Physics Wing
Happy Model Hr. Sec. School, Udhampur, J&K
Website: happyphysics.com
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Ch 27 Magnetic Field
and Magnetic Forces
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27.1 Magnetism
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Earth’s magnetic field
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N
S
Break apart
N
S
N
S
Break apart
N S
N S
N S
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N S
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27.2 Magnetic Field
Magnetic interactions:
1. A moving charge or
a current creates a
magnetic field in the
surrounding space
2. The magnitude field
exerts a force on
any other moving
charge or current
that is present in the
field
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F qv B
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Units of B-field
Unit of B-field is tesla
1 tesla = 1 T =1 N/Am
Another unit is gauss (G)
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27.3 Magnetic Field Lines and Magnetic
Flux
F qv B
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Magnetic Flux and Gauss’s Law for Magnetism
magnetic flux
through any closed
surface
B dA 0
magnetic flux
through a
surface
B B dA B cos dA B dA
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Example 27.2
The figure shows a flat surface with area 3cm2 in a
uniform B-field. If the magnetic flux through this area is
0.9mWb, Find the magnitude of B-field.
ANS:
B
B
A cos
0.9 103Wb
(3.0 104 m 2 )(cos 60)
6T
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27.4 Motion of Charged Particles in a
Magnetic Field
Motion of a charged
particle under the
action of a magnetic
field alone is always
motion with
constant speed
v2
F m
R
mv
R
qB
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Magnetic bottle
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Example 27.3
A magnetron in a microwave oven emits
electromagnetic waves with frequency f=2450MHz.
What magnetic field strength is required for electrons
to move in circular paths with this frequency?
ANS:
m
B
q
31
1
(9.1110 kg )(1.54 10 s )
1.60 1019 C
0.0877T
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10
27.5 Applications of Motion of Charged
Particles
Velocity Selector
Thomson’s e/m Experiment
Mass Spectrometers
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27.6 Magnetic Force on a Current-Carrying
Conductor
J nqvd
JA I
F IlB
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magnetic force on a
straight wire segment
F Il B
magnetic force on
an infinitesimal wire
section
dF I dl B
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27.7 Force and Torque on a Current
Loop
magnitude of torque
on a current loop
τ IBA sin
vector torque on a
current loop
τ μ B
potential energy for
a magnetic dipole
U μ B B cos
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27.8 The Direct-Current Motor
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27.9 The hall Effect
nq
J x By
Ez
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Magnetic interactions are fundamentally interactions
between moving charged particles. These interactions
are described by the vector magnetic field, denoted
by B .A particle with charge q moving with velocity v in
a magnetic field B experiences a force F that is
perpendicular to both v and B . The SI unit of magnetic
field is the tesla (1 T = 1 N/A.m). (See Example 28.1)
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A magnetic field can be represented graphically by
magnetic field lines. At each point a magnetic field
line is tangent to the direction of B at that point.
Where field lines are close together the field
magnitude is large, and vice versa.
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Magnetic fluxΦB through an area is defined in an
analogous way to electric flux. The SI unit of magnetic
flux is the weber (1 Wb = 1Tm2). The net magnetic flux
through any closed surface is zero (Gauss’s law for
magnetism). As a result, magnetic field lines always
close on themselves. (See Example 27.2)
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The magnetic force is always perpendicular to v ; a
particle moving under the action of a magnetic field
alone moves with constant speed. In a uniform field, a
particle with initial velocity perpendicular to the field
moves in a circle with radius R that depends on the
magnetic field moves in a circle with radius R that
depends on the magnetic field strength B and the
particle mass m, speed v, and charge q. (See
Examples 27.3 and 27.4)
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Crossed electric and magnetic fields can be used
as a velocity selector. The electric and magnetic
forces exactly cancel when v = E/B. (See
Examples 27.5 and 27.6)
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A straight segment of a conductor carrying current I
in a magnetic field B experiences a forceF that is
perpendicular to both B and the vector l, which points
in the direction of the current and has magnitude
equal to the length of the segment. A similar
relationship gives the force d F on an infinitesimal
current-carrying segment d l .
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A current loop with area A and current I in a uniform
magnetic fieldB experiences no net magnetic force,
but does experience a magnetic torque of magnitude
τ . The vector torque can be expressed in terms of
the magnetic moment IA of the loop, as can the
potential energy U of a magnetic moment in a
magnetic field B . The magnetic moment of a loop
depends only on the current and the area; it is
independent of the shape of the loop.
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In a dc motor a magnetic field exerts a torque on a
current in the rotor. Motion of the rotor through the
magnetic field causes and induced emf called a back
emf. For a series motor, in which the rotor coil is in
parallel with coils that produce the magnetic field, the
terminal voltage is the sum of the back emf and the
drop Ir across the internal resistance.
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The Hall effect is a potential difference perpendicular
to the direction of current in a conductor, when the
conductor is placed in a magnetic field. The Hall
potential is determined by the requirement that the
associated electric field must just balance the
magnetic force on a moving charge. Hall-effect
measurements can be used to determine the sigh of
charge carriers and their concentration n.
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