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MAGNETISM
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André-Marie Ampére is credited with the discovery of
electromagnetism, the relationship between electric
currents and magnetic fields.
Heinrich Hertz was the first to generate and detect
electromagnetic waves in the laboratory.
1 Magnetic Force acting on a charge q: [Newtons N]
F = qvBsinq
F = qv ´ B
F = force [N]
q = charge [C]
v = velocity [m/s]
B = magnetic field [T]
q = angle between v and B
2 Right-Hand Rule:
Fingers represent the direction of the
magnetic force B, thumb represents the direction of v (at
any angle to B), and the force F on a positive charge
emanates from the palm. The direction of a magnetic field
is from north to south. Use the left hand for a negative
charge.
Also, if a wire is grasped in the right hand with the thumb in
the direction of current flow, the fingers will curl in the
direction of the magnetic field.
In a solenoid with current flowing in the direction of curled
fingers, the magnetic field is in the direction of the thumb.
When applied to electrical flow caused by a changing
magnetic field, things get more complicated. Consider the
north pole of a magnet moving toward a loop of wire
(magnetic field increasing). The thumb represents the
north pole of the magnet, the fingers suggest current flow in
the loop. However, electrical activity will serve to balance
the change in the magnetic field, so that current will
actually flow in the opposite direction. If the magnet was
being withdrawn, then the suggested current flow would be
decreasing so that the actual current flow would be in the
direction of the fingers in this case to oppose the decrease.
Now consider a cylindrical area of magnetic field going into
a page. With the thumb pointing into the page, this would
suggest an electric field orbiting in a clockwise direction. If
the magnetic field was increasing, the actual electric field
would be CCW in opposition to the increase. An electron in
the field would travel opposite the field direction (CW) and
would experience a negative change in potential.
3 Force on a Wire in a Magnetic Field: [Newtons N]
F = BI esinq
F = I e ´ B
F = force [N]
B = magnetic field [T]
I = amperage [A]
e = length [m]
q = angle between B and the
direction of the current
4 Torque on a Rectangular Loop: [Newton·meters N·m]
t = NBIAsinq
N = number of turns
B = magnetic field [T]
I = amperage [A]
A = area [m2]
q = angle between B and the plane of the loop
5 Charged Particle in a Magnetic Field:
R = mv / qB
r = radius of rotational path
m = mass [kg]
v = velocity [m/s]
q = charge [C]
B = magnetic field [T]
6 Magnetic Field Around a Wire: [T]
B = m0I / 2pr
B = magnetic field [T]
m0 = the permeability of free space 4p×10-7 T·m/A
I = current [A]
r = distance from the center of the conductor
Magnetic Field at the center of an Arc: [T]
B = magnetic field [T]
m0 = the permeability of free space 4p×10-7 T·m/A
i = current [A]
Æ = the arc in radians
r = distance from the center of the conductor
Hall Effect:
Voltage across the width of a conducting ribbon due to a Magnetic Field:
(ne)Vw h = Bi
Vd Bw = Vw
ne = carrier charge density [C/m3]
Vw = voltage across the width [V]
h = thickness of the conductor [m]
B = magnetic field [T]
i = current [A]
vd = drift velocity [m/s]
w = width [m]
Force Between Two Conductors:
The force is attractive if the currents are in the same direction.
F = force [N]
e = length [m]
m0 = the permeability of free
space 4p×10-7T·m/A
I = current [A]
d = distance center to center [m]
Magnetic Field Inside of a Solenoid: [Teslas T]
B = m0 nI
B = magnetic field [T]
m0 = the permeability of free
space 4p×10-7 T·m/A
n = number of turns of wire per unit length [#/m]
I = current [A]
Magnetic Dipole Moment: [J/T]
m = NiA
m = the magnetic dipole moment [J/T]
N = number of turns of wire
i = current [A]
A = area [m2]
Magnetic Flux through a closed loop: [T·M2 or Webers]
j = BA cosq
B = magnetic field [T]
A = area of loop [m2]
q = angle between B and the perpen-dicular to the plane of the loop
Magnetic Flux
for a changing magnetic field: [T·M2 or Webers]
j = ∫ B× dA
B = magnetic field [T]
A = area of loop [m2]
A Cylindrical Changing Magnetic Field:
E = electric field [N/C]
r = radius [m]
t = time [s]
j = magnetic flux [T·m2 or Webers]
B = magnetic field [T]
A = area of magnetic field [m2]
dB/dt = rate of change of the magnetic field [T/s]
e= potential [V]
N = number of orbits
Faraday’s Law of Induction
states that the instantaneous emf induced in a circuit equals the rate of change of magnetic flux through the circuit. Michael Faraday made fundamental discoveries in magnetism, electricity, and light.
e = -N (Δ j / Δt)
N = number of turns
j = magnetic flux [T·m2]
t = time [s]
Lenz’s Law :
states that the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through a circuit
Motional emf
is induced when a conducting bar moves through a perpendicular magnetic field.
e = Bev
B = magnetic field [T]
e = length of the bar [m]
v = speed of the bar [m/s]
emf Induced in a Rotating Coil:
e = NABw sinwt.
N = number of turns
A = area of loop [m2]
B = magnetic field [T]
w = angular velocity [rad/s]
t = time [s]
Self-Induced emf in a Coil due to changing current:
e= -L(ΔI / Δt)
L = inductance [H]
I = current [A]
t = time [s]
Inductance per unit length
near the center of a solenoid:
L / e = m0 n2 A
L = inductance [H]
e = length of the solenoid [m]
m0 = the permeability of free space
4p×10-7 T·m/A
n = number of turns of wire per unit length [#/m]
A = area [m2]
Amperes' Law:
∫ B × ds = m0ienc
B = magnetic field [T]
m0 = the permeability of free space
4p×10-7 T·m/A
Ienc = current encircled by the loop[A]
Joseph Henry, American physicist, made improvements
to the electromagnet.
James Clerk Maxwell provided a theory showing the close relationship between electric and magnetic phenomena and predicted that electric and magnetic fields could move through space as waves.
J. J. Thompson is credited with the discovery of the
electron in 1897.
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