Post on 02-Dec-2014
Ain Shams University
Mathematics and Engineering Physics Department
Preparatory year
Magnetism course
First lecture
Dr. Wael Fikry And Dr. Hatem El-Refaei
Dr. Wael Fikry and Dr. Hatem El-Refaei 2
Course content Chapter 1: Magnetic field Chapter 2: Magnetic field of electric current Chapter 3: Electromagnetic induction Chapter 4: Magnetic properties of matter
Dr. Wael Fikry and Dr. Hatem El-Refaei 3
Course evaluation 300 Marks.
First term= 90 marks. First med term= 20 marks. Second term= 90 marks. Second med term= 20 marks. Lab exam= 60 marks. Sections+lab= 20 marks
190 marks
110 marks
Excellent (85%) = 255 marks
Dr. Wael Fikry and Dr. Hatem El-Refaei 4
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a uniform
magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 5
Applications
Maglev transrapid train (500Km/h)Motor (dynamo)
Mass spectrometerVan Allen belts
Dr. Wael Fikry and Dr. Hatem El-Refaei 6
History/people
Hans Oersted (1770-1851)
Andre Ampere (1775-1836)
Michael Faraday (1791-1867)
James Maxwell (1831-1879)
Dr. Wael Fikry and Dr. Hatem El-Refaei 7
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a uniform
magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 8
Electrostatic and Electrodynamics
Moving point charge
Produces B ?
Is affected by Magnetic force ?
Static point charge
Produces E rar
qE
24
Is affected by Coulomb’s force
Placed in external E
Placed in external B
extElectric EqF
Chapter 1
Chapter 2
Dr. Wael Fikry and Dr. Hatem El-Refaei 9
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a uniform
magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 10
Force induced by magnetic field Experimentally, one finds that, if a moving charge is
affected by a magnetic field, a force is exerted on the charge that is proportional to:
The charge q. The charge velocity v. The magnetic field density B. The sin of the angle between the velocity and B.
BvqF
sinBvqF
One finds also that the force direction is perpendicular to the plan containing v and B.
sinBvqF
Dr. Wael Fikry and Dr. Hatem El-Refaei 11
Force induced by magnetic field (continue)
BvqF
Positive chargeNegative charge
Dr. Wael Fikry and Dr. Hatem El-Refaei 12
Force induced by magnetic field (continue)
The direction of the force F is at right angle to the plan joining v,B.
The induced force is perpendicular to the motion direction, thus it doesn’t affect (by increasing or decreasing) the particle’s energy.
The direction of the force F is reversed if the direction of the velocity v is reversed.
The direction of the force F is reversed if the direction of the magnetic field B is reversed.
For the same v and B, two equal but opposite charges (an electron and a proton) particles are affected by forces of the same magnitude but opposite directions.
Dr. Wael Fikry and Dr. Hatem El-Refaei 13
Force induced by magnetic field (continue)
sinvq
FB
TeslameterAmper
Newton
ondsec/meterCoulomb
NewtonB
11mNAT
The units of B can be found from
Lab magnet produces a B in the range of few Tesla. Superconducting magnet can produce 30 Tesla. A smaller magnetic field unit – called guass – is defined as
GT 4101 The magnitude of earth’s magnetic field near the surface is
0.5G
Dr. Wael Fikry and Dr. Hatem El-Refaei 14
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a uniform
magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 15
Lorentz force
extElectric EqF
extMagnetic BvqF
Moving point charge
Produces B ?
Is affected by Magnetic force
Static point charge
Produces E rar
qE
24
Is affected by Coulomb’s force
Placed in external E
Placed in external B
Dr. Wael Fikry and Dr. Hatem El-Refaei 16
Lorentz force
extextLorentz BvqEqF
Thus, a moving charge placed in a magnetic and electric fields are affected by a total force called Lorentz’s force.
extextLorentz BvEqF
MagneticElectricLorentz FFF
Dr. Wael Fikry and Dr. Hatem El-Refaei 17
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a uniform
magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 18
The motion of a charged particle perpendicular to a uniform magnetic field
B inside
Thus for a given charged particle, the periodic time depends only on B
Radius of the pathqB
mvr
Periodic timev
r
Velocity
LengthT
2
Newton’s second law rmaF
r
mvqvBF
2
B
vqB
mvT
2
qB
mT 2 )Hz(
TfFrequency
1
Dr. Wael Fikry and Dr. Hatem El-Refaei 19
The motion of a charged particle perpendicular to a uniform magnetic field
Exp.: If a stream of protons enters a magnetic field at different velocities perpendicular to B:
Protons with higher velocity will rotate with larger radius (r). All protons will have the same periodic time (T).
Radius of the pathqB
mvr
qB
mT 2Periodic time
Dr. Wael Fikry and Dr. Hatem El-Refaei 20
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a uniform
magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 21
The motion of a charged particle inclined to a magnetic field
The normal component of the velocity (v) to the magnetic field B produces the circular motion.
The parallel component of the velocity (v||) to the magnetic field B produces linear motion
Radius of the pathqB
mvr
Periodic timeqB
m
v
rT
22
TvTimeVelocityd ||Pitch
||vvv
qB
mvd ||2
Dr. Wael Fikry and Dr. Hatem El-Refaei 22
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a magnetic field. Applications:
Speed selector. Cyclotron.
Dr. Wael Fikry and Dr. Hatem El-Refaei 23
Applications
Dr. Wael Fikry and Dr. Hatem El-Refaei 24
1- Velocity selector
E, B, and v are all perpendicular to each other. Different charged particles pass through the device
at different velocities. Particles with a certain velocity (v) that are affected
by electric force FE and magnetic force FB which are equal in magnitude and opposite in direction will emerge horizontally without deviation.
BELorentz FFFF
Velocity selector
B inside
BvqEq B
Ev
0 BvEq
0
0 BvqEq
Choosing the downward direction as the positive
direction.
Dr. Wael Fikry and Dr. Hatem El-Refaei 25
1- Velocity selector (continue)
Velocity selector
B inside
Any particle that doesn’t satisfy this relation will either:
Hit the upper or lower plate. Deviate upward or downward from the
horizontal direction and emerge from the device.
Dr. Wael Fikry and Dr. Hatem El-Refaei 26
2- The Cyclotron
27inch cyclotron in 1934Cyclotron was invented by Lawrence and Livingston
First prototype 1930
Dr. Wael Fikry and Dr. Hatem El-Refaei 27
2- The Cyclotron
Fermilab particle accelerator at Illinois.
Dr. Wael Fikry and Dr. Hatem El-Refaei 28
2- The Cyclotron
It is an instrument used to give high energy to charged particles.
The particles move in a vacuum chamber in two semicircular metal containers.
The D’s are hosted in a uniform magnetic field.
Dr. Wael Fikry and Dr. Hatem El-Refaei 29
2- The Cyclotron
Each time the particle crosses the gap between the D’s, the electric field is switched to the direction to accelerate its velocity .
Dr. Wael Fikry and Dr. Hatem El-Refaei 30
2- The Cyclotron (cont.)
2
2
1
m
RqBmKEmax
v
rt
Time to travel a semicircle of radius r
Tf
1The frequency of the alternating
electric field
2
2
1maxmax mvKE The total energy given
to the particle
RecallqB
mvr
m
BqRKE
222
2
1max
m
qBRv max
qB
m
t2
1
m
qB
2
1
qB
mvRr max
max
R is the radius of the cyclotron
Dr. Wael Fikry and Dr. Hatem El-Refaei 31
First lecture’s content Applications. History/People. Chapter 1: Magnetic field
Electrostatic and electrodynamics. Force induced on a point charge by magnetic field. Lorentz law. The motion of a charged particle perpendicular to a uniform
magnetic field. The motion of a charged particle inclined to a magnetic field. Applications:
Speed selector. Cyclotron.