Magnetism Lecture1

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


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


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.


Applications

Maglev transrapid train (500Km/h)Motor (dynamo)

Mass spectrometerVan Allen belts


History/people

Hans Oersted (1770-1851)

Andre Ampere (1775-1836)

Michael Faraday (1791-1867)

James Maxwell (1831-1879)








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








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


Force induced by magnetic field (continue)

BvqF

Positive chargeNegative charge



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.



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








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


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








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


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).


mvr

qB

mT 2Periodic time








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


mvr

Periodic timeqB

m

v

rT

22

TvTimeVelocityd ||Pitch

||vvv

qB

mvd ||2




magnetic field. The motion of a charged particle inclined to a magnetic field. Applications:



Applications


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.


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.


2- The Cyclotron

27inch cyclotron in 1934Cyclotron was invented by Lawrence and Livingston

First prototype 1930


2- The Cyclotron

Fermilab particle accelerator at Illinois.


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.


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 .


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




magnetic field. The motion of a charged particle inclined to a magnetic field. Applications:


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Magnetism Lecture1