CSS Physics Notes 2

I: Electricity and Magnetism…………………………………………………………….3
• Electric field due to point charges, Gauss’ law Electric potential and Poisson and
Laplace’s equation Dielectric medium and Polarization; Capacitance;
Moving charges and resulting magnetic field; Ampere’s law; Vector potential;
Magnetic properties of matter; Transient current; Faraday’s law of electromagnetic
induction; Alternating current and LRO circuit. Maxwell’s equations; Poynting
theorem and Poynting Vector. Maxwell's equations in integral and differential form.
II. Modern and Quantum Physics………………………………………………………68
• Operators and quantum states, observables, time dependent and independent
Schrodinger equation, angular momentum, spin-1/2 particle in a magnetic field,
wave mechanics, particle in a box, tunneling, one-dimensional harmonic oscillator,
Heisenber's uncertainty relationship and indeterminacy based on commutation
properties of operators, Bohr theory and quantum numbers including electron spin;
Pauli’s exclusion principle; Spectra of simple systems with one or two valence
electrons. Photo electric effect Compton scattering; pair production;
Lande’s g factor and Zeeman effect. Raman effect; Waves and particles and De
Broglie’s Hypothesis.
III. Solid State Physics…………………………………………………………………….135
• Crystal lattice and structure, Bravais lattice, free electron model, Band theory and
electron in a periodic potential, Fermi energy and density of states, n and p type
semiconductors, physics of the transistor and MOSFET, dielectric properties,
magnetic properties and origin of magnetism.
IV. Nuclear Physics…………………………………………………………………………180
• Structure of Nuclei; Radioactivity, , and decay. Methods of detection, Mass
Sepectrometer. Accelerators. Phenomenon of fission; reactor and nuclear
power, nuclear fusion and its application, Elementary particles and their properties

Electricity and Magnetism:
Electricity and magnetism:
Electricity and magnetism are manifestations of a single underlying electromagnetic force.
Electromagnetism is a branch of physical science that describes the interactions of electricity
and magnetism, both as separate phenomena and as a singular electromagnetic force.
Amagnetic field is created by a moving electric current and a magnetic field can induce
movement of charges (electric current). The rules of electromagnetism also explain
geomagnetic and electromagnetic phenomena by explaining how charged particles of atoms
interact.
Before the advent of technology, electromagnetism was perhaps most strongly experienced
in the form of lightning , and electromagnetic radiation in the form of light. Ancient man kindled
fires that he thought were kept alive in trees struck by lightning. Magnetism has long been
employed for navigation in the compass. In fact, it is known that Earth's magnetic poles have
exchanged positions in the past.
Some of the rules of electrostatics, the study of electric charges at rest, were first noted by the
ancient Romans, who observed the way a brushed comb would attract particles. It is now
known that electric charges occur in two different forms, positive charges and negative
charges. Like charges repel each other, and differing types attract.
The force that attract positive charges to negative charges weakens with distance, but is
intrinsically very strong—up to 40 times stronger than the pull of gravity at the surface of the
earth. This fact can easily be demonstrated by a small magnet that can hold or suspend an
object. The small magnet exerts a force at least equal to the pull of gravity from the entire
Earth.
The fact that unlike charges attract means that most of this force is normally neutralized and
not seen in full strength. The negative charge is generally carried by the atom's electrons,
while the positive resides with the protons inside the atomic nucleus. Other less known
particles can also carry charge. When the electrons of a material are not tightly bound to the
atom's nucleus, they can move from atom to atom and the substance, called a conductor, can
conduct electricity. Conversely, when the electron binding is strong, the material resists
electron flow and is an insulator.
When electrons are weakly bound to the atomic nucleus, the result is a semiconductor, often
used in the electronics industry. It was not initially known if the electric current carriers were
positive or negative, and this initial ignorance gave rise to the convention that current flows
from the positive terminal to the negative. In reality we now know that the electrons actually
flow from the negative to the positive.
Electromagnetism is the theory of a unified expression of an underlying force, the
electromagnetic force. This is seen in the movement of electric charge, that gives rise to
magnetism (the electric current in a wire being found to deflect a compass needle), and it was
Scottish physicist James Clerk Maxwell (1831–1879), who published a unifying theory of
electricity and magnetism in 1865. The theory arose from former specialized work by German
mathematician Carl Fredrich Gauss (1777–1855), French physicist Charles Augustin de
Coulomb (1736–1806), French scientist André Marie Ampère

(1775–1836), English physicist Michael Faraday (1791–1867), American scientist and
statesman Benjamin Franklin (1706–1790), and German physicist and mathematician Georg
Simon Ohm (1789–1854). However, one factor that did not contradict the experiments was
added to the equations by Maxwell to ensure the conservation of charge. This was done on
the theoretical grounds that charge should be a conserved quantity, and this addition led to
the prediction of a wave phenomena with a certain anticipated velocity. Light, with the
expected velocity, was found to be an example of this electro-magnetic radiation.
Light had formerly been thought of as consisting of particles (photons) by Newton, but the
theory of light as particles was unable to explain the wave nature of light (diffraction and the
like). In reality, light displays both wave and particle properties. The resolution to this duality
lies in quantum theory , where light is neither particles nor wave, but both. It propagates as a
wave without the need of a medium and interacts in the manner of a particle. This is the basic
nature of quantum theory.
Classical electromagnetism, useful as it is, contains contradictions (acausality) that make it
incomplete and drive one to consider its extension to the area of quantum physics , where
electromagnetism, of all the fundamental forces of nature, it is perhaps the best understood.
There is much symmetry between electricity and magnetism. It is possible for electricity to give
rise to magnetism, and symmetrically for magnetism to give rise to electricity (as in the
exchanges within an electric transformer). It is an exchange of just this kind that constitutes
electromagnetic waves. These waves, although they don't need a medium of propagation, are
slowed when traveling through a transparent substance.
Electromagnetic waves differ from each other only in amplitude, frequency, and orientation
(polarization). Laser beams are particular in being very coherent, that is, the radiation is of one
frequency, and the waves coordinated in motion and direction. This permits a highly
concentrated beam that is used not only for its cutting abilities, but also in electronic data
storage, such as in CD-ROMs.
The differing frequency forms are given a variety of names, from radio waves at very low
frequencies through light itself, to the high frequency x rays and gamma rays.
The unification of electricity and magnetism allows a deeper understanding of physical
science, and much effort has been put into further unifying the four forces of nature (e.g., the
electromagnetic, weak, strong, and gravitational forces. The weak force has now been unified
with electromagnetism, called the electroweak force. There are research programs attempting
to collect data that may lead to a unification of the strong force with the electroweak force in a
grand unified theory, but the inclusion of gravity remains an open problem.
Maxwell's theory is in fact in contradiction with Newtonian mechanics, and in trying to find the
resolution to this conflict, Einstein was lead to his theory of special relativity. Maxwell's
equations withstood the conflict, but it was Newtonian mechanics that were corrected by
relativistic mechanics. These corrections are most necessary at velocities, close to the speed
of light.
Paradoxically, magnetism is a counter example to the frequent claims that relativistic effects
are not noticeable for low velocities. The moving charges that compose an electric current in
a wire might typically only be traveling at several feet per second (walking speed), and the
resulting Lorentz contraction of special relativity is indeed minute. However, the electrostatic
forces at balance in the wire are of such great magnitude, that this small contraction of the

moving (negative) charges exposes a residue force of real world magnitude, namely the
magnetic force. It is in exactly this way that the magnetic force derives from the electric.
Special relativity is indeed hidden in Maxwell's equations, which were known before special
relativity was understood or separately formulated by Einstein.
Electricity at high voltages can carry energy across extended distances with little loss.
Magnetism derived from that electricity can then power vast motors. But electromagnetism
can also be employed in a more delicate fashion as a means of communication, either with
wires (as in the telephone), or without them (as in radio communication). It also drives motors
and provides current for electronic and computing devices.
Electric Field Due to Point Charges:
Electric field is defined as the electric force per unit charge. The direction of the field is taken
to be the direction of the force it would exert on a positive test charge. The electric field is
radially outward from a positive charge and radially in toward a negative point charge.

The electric field of a point charge can be obtained from Coulomb's law:
The electric field is radially outward from the point charge in all directions. The circles
represent spherical equipotential surfaces.
The electric field from any number of point charges can be obtained from a vector sum of the
individual fields. A positive number is taken to be an outward field; the field of a negative
charge is toward it.
This electric field expression can also be obtained by applying Gauss' law.

Point charges, such as electrons, are among the fundamental building blocks of matter.
Furthermore, spherical charge distributions (like on a metal sphere) create external electric
fields exactly like a point charge. The electric potential due to a point charge is, thus, a case
we need to consider. Using calculus to find the work needed to move a test charge q from a
large distance away to a distance of r from a point charge Q, and noting the connection
between work and potential , it can be shown that the electric potential V of a point charge is
E is a vector quantity
Magnitude & direction vary with
position--but depend on object w/
charge Q setting up the field
E-field exerts a force on other point charges
Gauss’ law Electric Potential:
Flux of an Electric Field:
In this lecture we introduce “Gauss’s law” which happens to be equivalent to Coulomb’s law.
However, under certain circumstances it turn out to be much easier to deal with than
Coulomb’s law. Before stating the law, we will introduce the concept of “flux” of an electric
field. As has been mentioned during our discussion of vector calculus, the concept of flux
arises from fluid dynamics. If we have a fluid flowing past a surface, the flux of fluid through
the surface not only depends on the velocity of the fluid, it also depends on the magnitude of
the area and the orientation of the area with respect to the direction of the velocity.
We had seen earlier that an infinitesimal surface can be looked upon as a vector with the
magnitude equal to the area and the direction along the outward normal to the surface
In the figure above we see electric field lines passing through a surface S, the direction of the
electric field making an angle θ with the normal to the surface. The flux of the electric field is
defined as In performing the sum, one has to know the electric field at every point on the
surface and the angle that the field makes with the outward normal at that point. If the electric
field is constant, the flux becomes Ecos@dS .

Solid Angle :
We are familiar with the concept of an angle in two dimensions. Loosely speaking an agle is
a measure of divergence or spread between two straight lines. Suppose the lines meet at the
point O. With O as the centre, if we draw arc of a circle of radius R, the two straight lines will
contain an arc of the circle
Note that the circular arc is along the transverse direction to the two lines. Suppose, instead,
we draw an arbitrary curve (shown in red) which cuts the two lines, the length L is to be taken
along the transverse projection of this curve. Note that, being ratio of two lengths, an angle
is dimensionless. However, we conventionally measure it in terms of a unit which could be a
degree or a radian or a grade.
The concept of solid angle is straightforward extension of this concept in three dimensions.
Solid angle is the angle that an arbitrary area makes at a point. What is to be done is to
describe a right circular cone of length R about the point P. The ratio of the transverse area
intercepted by the cone to the square of the distance from the point P is a measure of the solid
angle. Like in the case of angle in two dimensions, we have to take a transverse area. Like
ordinary angle, a solid angle is dimensionless but is measured in a unit called “steradian”

Consider a surface S. What is the solid angle subtended by the surface at the point P. We
draw tangents from P to the edge of the surface. If the surface area is transverse (i.e. the
area is a part of the sphere intercepted by such tangents), the solid angle is simply the ratio
of the part of the sphere intercepted by the tangents to the distance squared. For other surface,
transverse projections have to be taken.
Book has been attached for more details:
Gauss’s law :
Consider the following situations. Suppose we have a volume of arbitrary shape defined by a
surface S with a charge q embedded therein. Infinitesimal surface area dS at a position with
respect to thecharge. The surface element makes a solid angle at the position of the charge.
The electric fieldat dS due to the charge q is along the radial direction and is given by . If the
angle between the normal to the element and the position vector is θ, then is the projection
of dS along a direction perpendicular to . Thus the flux of the electric field out of this element
is . Notice that the flux due to the area element depends on the solid angle that it subtends
at the position of the charge. Since the charge is embedded inside, at every place on the
surface, the radial direction is outward and the normal to the surface makes an acute angle
with the radial direction at that point. Thus the total flux in this situation is given by
Equations:
The measure of the angle (in radian measure) is then the ratio of the length L of the arc to
the radius of the circle. since the total solid angle subtended at q by the entire surface is 4π.
Suppose, instead, the charge q is somewhere outside the volume. If we draw rays of a cone
from the charge on to the volume, they will intersect the surface at two places, with the normal
of one of the surface elements making an acute angle with and the other making an obtuse
angle. Thus for every positive solid angle there is an equal and opposite negative solid angle
and the total flux adds up to zero.
Thus the flux out of a surface equals if the charge is enclosed by the surface and equals zero
if it is outside. Using superposition principle, one can, by very similar argument, conclude that
for multiple charges the result would be true as well, and we then have,
For Further Details File Attached with Email.

Poisson Equations:
Poisson’s equation is derived from Coulomb’s law and Gauss’s theorem. It is a par-tial
differential equation with broad utility in electrostatics, mechanical engineer-ing, and
theoretical physics. It is named after the French mathematician, geometer and physicist
Sim´eon-Denis Poisson (1781-1840). Charles Augustin Coulomb (1736-1806) was a French
physicist who discovered an inverse relationship on the force between charges and the square
of its distance. Karl Friedrich Gauss (1777-1855) was a German mathematician who also
proved the fundamental theorems of algebra and arithmetic
PDF File Attached for Details:
Laplace’s Equation:
Laplace’s equation, second-order partial differential equation widely useful in physics because
its solutions R (known as harmonic functions) occur in problems of electrical, magnetic, and
gravitational potentials, of steady-state temperatures, and of hydrodynamics. The equation
was discovered by the French mathematician and astronomer Pierre-Simon Laplace (1749–
1827).
Laplace’s equation states that the sum of the second-order partial derivatives of R, the
unknown function, with respect to the Cartesian coordinates, equals zero.
The sum on the left often is represented by the expression ∇2R, in which the symbol ∇2 is
called the Laplacian, or the Laplace operator.
Many physical systems are more conveniently described by the use of spherical or cylindrical
coordinate systems. Laplace’s equation can be recast in these coordinates; for example, in
cylindrical coordinates, Laplace’s equation is
:
A useful approach to the calculation of electric potentials is to relate that potential to the charge
density which gives rise to it. The electric field is related to the charge density by the
divergence relationship
and the electric field is related to the electric potential by a gradient relationship

Therefore the potential is related to the charge density by Poisson's equation
In a charge-free region of space, this becomes LaPlace's equation
This mathematical operation, the divergence of the gradient of a function, is called the
LaPlacian. Expressing the LaPlacian in different coordinate systems to take advantage of the
symmetry of a charge distribution helps in the solution for the electric potential V. For example,
if the charge distribution has spherical symmetry, you use the LaPlacian in spherical polar
coordinates.
Potential of a Uniform Sphere of Charge
Since the potential is a scalar function, this approach has advantages over trying to calculate
the electric field directly. Once the potential has been calculated, the electric field can be
computed by taking the gradient of the potential.
The use of Poisson's and Laplace's equations will be explored for a uniform sphere
of charge. In spherical polar coordinates, Poisson's equation takes the form:

but since there is full spherical symmetry here, the derivatives
with respect to θ and φ must be zero, leaving the form
Examining first the region outside the sphere, Laplace's law
applies.
Since the zero of potential is arbitrary, it is reasonable to choose the zero of potential
at infinity, the standard practice with localized charges. This gives the value b=0.
Since the sphere of charge will look like a point charge at large distances, we may
conclude that
so the solution to LaPlace's law outside the sphere is
Now examining the potential inside the sphere, the potential must have a term of
order r2
to give a constant on the left side of the equation, so the solution is of the
form
Substituting into Poisson's equation gives
Now to meet the boundary conditions at the surface of the sphere, r=R

The full solution for the potential inside the sphere from Poisson's equation is
Dielectric Medium:
Dielectric, insulating material or a very poor conductor of electric current. When dielectrics are
placed in an electric field, practically no current flows in them because, unlike metals, they
have no loosely bound, or free, electrons that may drift through the material. Instead, electric
polarization occurs. The positive charges within the dielectric are displaced minutely in the
direction of the electric field, and the negative charges are displaced minutely in the direction
opposite to the electric field. This slight separation of charge, or polarization, reduces the
electric field within the dielectric.
The presence of dielectric material affects other electrical phenomena. The force between two
electric charges in a dielectric medium is less than it would be in a vacuum, while the quantity
of energy stored in an electric field per unit volume of a dielectric medium is greater. The
capacitance of a capacitor filled with a dielectric is greater than it would be in a vacuum. The
effects of the dielectric on electrical phenomena are described on a large, or macroscopic
scale by employing such concepts as dielectric constant, permittivity (qq.v.), and polarization.
A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied
electric field. When a dielectric is placed in an electric field, electric charges do not flow through
the material as they do in an electrical conductor but only slightly shift from their average
equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive
charges are displaced in the direction of the field and negative charges shift in the opposite
direction. This creates an internal electric field that reduces the overall field within the dielectric
itself.If a dielectric is composed of weakly bonded molecules, those molecules not only
become polarized, but also reorient so that their symmetry axes align to the field.
The study of dielectric properties concerns storage and dissipation of electric and magnetic
energy in materials. Dielectrics are important for explaining various phenomena in electronics,
optics, solid-state physics, and cell biophysics.
Electric susceptibility:
The electric susceptibility χe of a dielectric material is a measure of how easily it polarizes in
response to an electric field. This, in turn, determines the electric permittivity of the material
and thus influences many other phenomena in that medium, from the capacitance of
capacitors to the speed of light.
It is defined as the constant of proportionality (which may be a tensor) relating an electric field
E to the induced dielectric polarization density P such that

Dielectric Polarization:
Dipolar polarization is a polarization that is either inherent to polar molecules (orientation
polarization), or can be induced in any molecule in which the asymmetric distortion of the
nuclei is possible (distortion polarization). Orientation polarization results from a permanent
dipole, e.g., that arising from the 104.45° angle between the asymmetric bonds between
oxygen and hydrogen atoms in the water molecule, which retains polarization in the absence
of an external electric field. The assembly of these dipoles forms a macroscopic polarization.
When an external electric field is applied, the distance between charges within each
permanent dipole, which is related to chemical bonding, remains constant in orientation
polarization; however, the direction of polarization itself rotates. This rotation occurs on a
timescale that depends on the torque and surrounding local viscosity of the molecules.
Because the rotation is not instantaneous, dipolar polarizations lose the response to electric
fields at the highest frequencies. A molecule rotates about 1 radian per picosecond in a fluid,
thus this loss occurs at about 1011 Hz (in the microwave region). The delay of the response
to the change of the electric field causes friction and heat.
When an external electric field is applied at infrared frequencies or less, the molecules are
bent and stretched by the field and the molecular dipole moment changes. The molecular
vibration frequency is roughly the inverse of the time it takes for the molecules to bend, and
this distortion polarization disappears above the infrared.

Polarization:
Polarization, property of certain electromagnetic radiations in which the direction and
magnitude of the vibrating electric field are related in a specified way.
Light waves are transverse: that is, the vibrating electric vector associated with each wave is
perpendicular to the direction of propagation. A beam of unpolarized light consists of waves
moving in the same direction with their electric vectors pointed in random orientations about
the axis of propagation. Plane polarized light consists of waves in which the direction of
vibration is the same for all waves. In circular polarization the electric vector rotates about the
direction of propagation as the wave progresses. Light may be polarized by reflection or by
passing it through filters, such as certain crystals, that transmit vibration in one plane but not
in others.
Understanding and manipulating the polarization of light is crucial for many optical
applications. Optical design frequently focuses on the wavelength and intensity of light, while
neglecting its polarization. Polarization, however, is an important property of light that affects
even those optical systems that do not explicitly measure it. The polarization of light affects
the focus of laser beams, influences the cut-off wavelengths of filters, and can be important to
prevent unwanted back reflections. It is essential for many metrology applications such as
stress analysis in glass or plastic, pharmaceutical ingredient analysis, and biological
microscopy. Different polarizations of light can also be absorbed to different degrees by
materials, an essential property for LCD screens, 3D movies, and your glare-reducing
sunglasses.
Understanding polarization
Light is an electromagnetic wave, and the electric field of this wave oscillates perpendicularly
to the direction of propagation. Light is called unpolarized if the direction of this electric field
fluctuates randomly in time. Many common light sources such as sunlight, halogen lighting,
LED spotlights, and incandescent bulbs produce unpolarized light. If the direction of the
electric field of light is well defined, it is called polarized light. The most common source of
polarized light is a laser.
Depending on how the electric field is oriented, we classify polarized light into three types of
polarizations:
Linear polarization: the electric field of light is confined to a single plane along the direction
of propagation.

Figure 1: The electric field of linearly polarized light is confined to a single plane along the
direction of propagation.
Circular polarization: the electric field of light consists of two linear components that are
perpendicular to each other, equal in amplitude, but have a phase difference of π/2. The
resulting electric field rotates in a circle around the direction of propagation and, depending
on the rotation direction, is called left- or right-hand circularly polarized light.

the direction of propagation.
Figure 2: The electric field of circularly polarized light consists of two perpendicular, equal in
amplitude, linear components that have a phase of difference of π/2. The resulting electric
field describes a circle

Elliptical polarization: the electric field of light describes an ellipse. This results from the
combination of two linear components with differing amplitudes and/or a phase difference that
is not π/2. This is the most general description of polarized light, and circular and linear
polarized light can be viewed as special cases of elliptically polarized light.
Figure 3: The electric field of elliptically polarized light consists of two perpendicular linear
components with any amplitude and any phase difference. The resulting electric field
describes an ellipse.
The two orthogonal linear polarization states that are most important for reflection and
transmission are referred to as p- and s-polarization. P-polarized (from the German parallel)
light has an electric field polarized parallel to the plane of incidence, while s-polarized (from
the German senkrecht) light is perpendicular to this plane.

Figure 4: P and S are linear polarizations defined by their relative orientation to the plane of
incidence.
Manipulating Polarization:
Polarizers
In order to select a specific polarization of light, polarizers are used. Polarizers can be broadly
divided into reflective, dichroic, and birefringent polarizers. More detailed information on which
type of polarizer is right for your application can be found in our Polarizer Selection Guide.
Reflective polarizers transmit the desired polarization while reflecting the rest. Wire grid
polarizers are a common example of this, consisting of many thin wires arranged parallel to
each other. Light that is polarized along these wires is reflected, while light that is polarized
perpendicular to these wires is transmitted. Other reflective polarizers use Brewster’s angle.
Brewster’s angle is a specific angle of incidence under which only s-polarized light is reflected.
The reflected beam is s-polarized and the transmitted beam becomes partially p-polarized.
Dichroic polarizers absorb a specific polarization of light, transmitting the rest; modern
nanoparticle polarizers are dichroic polarizers.
Birefringent polarizers rely on the dependence of the refractive index on the polarization of
light. Different polarizations will refract at different angles and this can be used to select certain
polarizations of light.
Unpolarized light can be considered a rapidly varying random combination of p- and s-
polarized light. An ideal linear polarizer will only transmit one of the two linear polarizations,
reducing the initial unpolarized intensity I0 by half,
(1)
I=I02I=I02
For linearly polarized light with intensity I0, the intensity transmitted through an ideal
polarizer, I, can be described by Malus’ law,
(2)
I=I0cos2θ
Where θ is the angle between the incident linear polarization and the polarization axis. We
see that for parallel axes, 100% transmission is achieved, while for 90° axes, also known as
crossed polarizers, there is 0% transmission. In real world applications the transmission never
reaches exactly 0%, therefore, polarizers are characterized by an extinction ratio, which can
be used to determine the actual transmission through two crossed polarizers.
Waveplates:
While polarizers select certain polarizations of light, discarding the other polarizations, ideal
waveplates modify existing polarizations without attenuating, deviating, or displacing the
beam. They do this by retarding (or delaying) one component of polarization with respect to
its orthogonal component. To help you determine which waveplate is best for your application,
read Understanding Waveplates. Correctly chosen waveplates can convert any polarization

state into a new polarization state, and are most often used to rotate linear polarization, to
convert linearly polarized light to circularly polarized light or vice versa.
Applications
Implementing polarization control can be useful in imaging applications. By placing a linear
polarizer over the light source, the lens, or both, it is possible to eliminate glare and hot spots
from reflective objects or bring out surface defects.
Using Polarizers to Reduce Glare
Figure 5: To learn more about using polarizers to reduce glare, read Successful Light
Polarization Techniques.
Material stress can be quantified in transparent objects using the photoelastic effect. Stressed
material becomes birefringent, and the stress and its related birefringence can be measured
by using polarized light.
Figure 6: For more information on using polarization to measure stress, read Successful Light
Polarization Techniques or Contact Us.
Polarization is also very important in the chemical, pharmaceutical, and food and beverage
industries. Many important chemical compounds, such as active pharmaceutical ingredients
or sugar, are “optically active” and rotate polarized light. The amount of rotation is determined
by the nature and the concentration of the compound, allowing polarimetry to detect and
quantify these compounds.
Polarization by Scattering
Polarization also occurs when light is scattered while traveling through a medium. When light
strikes the atoms of a material, it will often set the electrons of those atoms into vibration. The
vibrating electrons then produce their own electromagnetic wave that is radiated outward in

all directions. This newly generated wave strikes neighboring atoms, forcing their electrons
into vibrations at the same original frequency. These vibrating electrons produce another
electromagnetic wave that is once more radiated outward in all directions. This absorption and
reemission of light waves causes the light to be scattered about the medium. (This process of
scattering contributes to the blueness of our skies, a topic to be discussed later.) This
scattered light is partially polarized. Polarization by scattering is observed as light passes
through our atmosphere. The scattered light often produces a glare in the skies.
Photographers know that this partial polarization of scattered light leads to photographs
characterized by a washed-out sky. The problem can easily be corrected by the use of a
Polaroid filter. As the filter is rotated, the partially polarized light is blocked and the glare is
reduced. The photographic secret of capturing a vivid blue sky as the backdrop of a beautiful
foreground lies in the physics of polarization and Polaroid filters.
Applications of Polarization
Polarization has a wealth of other applications besides their use in glare-reducing sunglasses.
In industry, Polaroid filters are used to perform stress analysis tests on transparent plastics.
As light passes through a plastic, each color of visible light is polarized with its own orientation.
If such a plastic is placed between two polarizing plates, a colorful pattern is revealed. As the
top plate is turned, the color pattern changes as new colors become blocked and the formerly
blocked colors are transmitted. A common Physics demonstration involves placing a plastic
protractor between two Polaroid plates and placing them on top of an overhead projector. It is
known that structural stress in plastic is signified at locations where there is a large
concentration of colored bands. This location of stress is usually the location where structural
failure will most likely occur. Perhaps you wish that a more careful stress analysis were
performed on the plastic case of the CD that you recently purchased.
Polarization is also used in the entertainment industry to produce and show 3-D movies.
Three-dimensional movies are actually two movies being shown at the same time through two
projectors. The two movies are filmed from two slightly different camera locations. Each
individual movie is then projected from different sides of the audience onto a metal screen.
The movies are projected through a polarizing filter. The polarizing filter used for the projector
on the left may have its polarization axis aligned horizontally while the polarizing filter used for
the projector on the right would have its polarization axis aligned vertically. Consequently,
there are two slightly different movies being projected onto a screen. Each movie is cast by
light that is polarized with an orientation perpendicular to the other movie. The audience then
wears glasses that have two Polaroid filters. Each filter has a different polarization axis - one
is horizontal and the other is vertical. The result of this arrangement of projectors and filters is
that the left eye sees the movie that is projected from the right projector while the right eye
sees the movie that is projected from the left projector. This gives the viewer a perception of
depth.
Our model of the polarization of light provides some substantial support for the wavelike nature
of light. It would be extremely difficult to explain polarization phenomenon using a particle view
of light. Polarization would only occur with a transverse wave. For this reason, polarization is
one more reason why scientists believe that light exhibits wavelike behavior.
Polarization by Refraction
Polarization can also occur by the refraction of light. Refraction occurs when a beam of light
passes from one material into another material. At the surface of the two materials, the path
of the beam changes its direction. The refracted beam acquires some degree of polarization.
Most often, the polarization occurs in a plane perpendicular to the surface. The polarization of

refracted light is often demonstrated in a Physics class using a unique crystal that serves as
a double-refracting crystal. Iceland Spar, a rather rare form of the mineral calcite, refracts
incident light into two different paths. The light is split into two beams upon entering the crystal.
Subsequently, if an object is viewed by looking through an Iceland Spar crystal, two images
will be seen. The two images are the result of the double refraction of light. Both refracted light
beams are polarized - one in a direction parallel to the surface and the other in a direction
perpendicular to the surface. Since these two refracted rays are polarized with a perpendicular
orientation, a polarizing filter can be used to completely block one of the images. If the
polarization axis of the filter is aligned perpendicular to the plane of polarized light, the light is
completely blocked by the filter; meanwhile the second image is as bright as can be. And if
the filter is then turned 90-degrees in either direction, the second image reappears and the
first image disappears. Now that's pretty neat observation that could never be observed if light
did not exhibit any wavelike behavior.
Polarization by Reflection:
Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces. The
extent to which polarization occurs is dependent upon the angle at which the light approaches
the surface and upon the material that the surface is made of. Metallic surfaces reflect light
with a variety of vibrational directions; such reflected light is unpolarized. However, nonmetallic
surfaces such as asphalt roadways, snowfields and water reflect light such that there is a large
concentration of vibrations in a plane parallel to the reflecting surface. A person viewing
objects by means of light reflected off of nonmetallic surfaces will often perceive a glare if the
extent of polarization is large. Fishermen are familiar with this glare since it prevents them
from seeing fish that lie below the water. Light reflected off a lake is partially polarized in a
direction parallel to the water's surface. Fishermen know that the use of glare-reducing
sunglasses with the proper polarization axis allows for the blocking of this partially polarized
light. By blocking the plane-polarized light, the glare is reduced and the fisherman can more
easily see fish located under the water.

Capacitance:
Capacitance, property of an electric conductor, or set of conductors, that is measured by the
amount of separated electric charge that can be stored on it per unit change in electrical
potential. Capacitance also implies an associated storage of electrical energy. If electric
charge is transferred between two initially uncharged conductors, both become equally
charged, one positively, the other negatively, and a potential difference is established between
them. The capacitance C is the ratio of the amount of charge q on either conductor to the
potential difference V between the conductors, or simply C = q/V.
In both the practical and the metre–kilogram–second scientific systems, the unit of electric
charge is the coulomb and the unit of potential difference is the volt, so that the unit of
capacitance—named the farad (symbolized F)—is one coulomb per volt. One farad is an
extremely large capacitance. Convenient subdivisions in common use are one-millionth of a
farad, called a microfarad (μF), and one-millionth of a microfarad, called a picofarad (pF; older
term, micromicrofarad, μμF). In the electrostatic system of units, capacitance has dimensions
of distance.
Capacitance in electric circuits is deliberately introduced by a device called a capacitor. It was
discovered by the Prussian scientist Ewald Georg von Kleist in 1745 and independently by the
Dutch physicist Pieter van Musschenbroek at about the same time, while in the process of
investigating electrostatic phenomena. They discovered that electricity obtained from an
electrostatic machine could be stored for a period of time and then released. The device, which
came to be known as the Leyden jar, consisted of a stoppered glass vial or jar filled with water,
with a nail piercing the stopper and dipping into the water. By holding the jar in the hand and
touching the nail to the conductor of an electrostatic machine, they found that a shock could
be obtained from the nail after disconnecting it, by touching it with the free hand. This reaction
showed that some of the electricity from the machine had been stored.
A simple but fundamental step in the evolution of the capacitor was taken by the English
astronomer John Bevis in 1747 when he replaced the water by metal foil forming a lining on
the inside surface of the glass and another covering the outside surface. This form of the
capacitor with a conductor projecting from the mouth of the jar and touching the lining had, as
its principal physical features, two conductors of extended area kept nearly equally separated
by an insulating, or dielectric, layer made as thin as practicable. These features have been
retained in every modern form of capacitor.
A capacitor, also called a condenser, is thus essentially a sandwich of two plates of conducting
material separated by an insulating material, or dielectric. Its primary function is to store

electrical energy. Capacitors differ in the size and geometrical arrangement of the plates and
in the kind of dielectric material used. Hence, they have such names as mica, paper, ceramic,
air, and electrolytic capacitors. Their capacitance may be fixed or adjustable over a range of
values for use in tuning circuits.
The energy stored by a capacitor corresponds to the work performed (by a battery, for
example) in creating opposite charges on the two plates at the applied voltage. The amount
of charge that can be stored depends on the area of the plates, the spacing between them,
the dielectric material in the space, and the applied voltage.
A capacitor incorporated in an alternating-current (AC) circuit is alternately charged and
discharged each half cycle. The time available for charging or discharging thus depends on
the frequency of the current, and if the time required is greater than the length of the half cycle,
the polarization (separation of charge) is not complete. Under such conditions, the dielectric
constant appears to be less than that observed in a direct-current circuit and to vary with
frequency, becoming lower at higher frequencies. During the alternation of polarity of the
plates, the charges must be displaced through the dielectric first in one direction and then in
the other, and overcoming the opposition that they encounter leads to a production of heat
known as dielectric loss, a characteristic that must be considered when applying capacitors to
electrical circuits, such as those in radio and television receivers. Dielectric losses depend on
frequency and the dielectric material.
Except for the leakage (usually small) through the dielectric, no current flows through a
capacitor when it is subject to a constant voltage. Alternating current will pass readily,
however, and is called a displacement current (q.v.).
Capacitors are used to store and quickly release large amounts of electrical energy. In this
lesson, we will learn how capacitors are created and used and how your body can function as
a capacitor.
What is Capacitance?
Capacitance is the ability to store electrical energy. Almost all things, including you, can store
some electrical energy and therefore have capacitance. When you rub your feet across a
carpet, charged particles called electrons can be transferred from the carpet to you. When
positive and negative charges are separated, the stored electrical energy increases. The
charges you have picked up from the carpet give you electrical energy that you store until you
touch something like a metal doorknob or another person that allows the energy to be
released. You feel this as a mild shock as the energy leaves your body.
Capacitors
Although the ability to store some electrical energy is common, devices called capacitors are
purposely designed to store large amounts of electrical energy. A typical capacitor consists of
two conducting surfaces (usually metal plates) separated by an insulating material like air,
rubber, or paper. This insulating material is called a dielectric.
In this parallel plate capacitor, two metal conducting plates are separated by a thin dielectric
(electrical insulator)
Capacitor
The capacitor can be charged by connecting one plate to the positive terminal of a battery and
the other to the negative terminal. The electric field produced by the battery causes electrons
to flow towards the positive terminal of the battery and away from the negative terminal. This

causes the two capacitor plates to become charged. One will be positively charged and the
other will be negatively charged. The insulating material keeps the charges from crossing over
from one plate to the other and allows the capacitor to store electrical energy. If it is
disconnected from the battery, the charges will remain stored in the capacitor until it is
connected to another electric unit.
Some typical capacitors used in electric circuits capacitors
How to Calculate Capacitance of a Capacitor:
The capacitance of the capacitor tells you how much charge it can store when connected to a
particular battery and is measured in units of farads. The capacitance (C) of a capacitor can
be determined by measuring the amount of charge stored on each plate (Q) when it is
connected to a battery with a certain voltage (V).
C = Q/V
For example, if we connected a capacitor to a 9 volt battery and measured that it stored 9
coulombs of charge, its capacitance would be 1 farad.
Uses of Capacitors
Capacitors are used in many devices that require electrical energy to be released quickly, like
camera flashes and computer keyboards. They are also used in circuits that are designed to
filter and amplify electronic signals. These circuits are found in radios, music amplifiers, and
medical devices. Here's a more specific example of a medical device that uses capacitors:

ECG:
This electrocardiogram (ECG) device measures the electric potential of the human heart. It
uses capacitors to filter out other electrical signals so that the electrical activity of the heart
can be monitored.
This electrocardiogram (ECG) device measures the electric potential of the human heart. It uses
capacitors to filter out
Moving Charges and Resulting Magnetic Field:
What is the mechanism by which one magnet exerts a force on another? The answer is related
to the fact that all magnetism is caused by current, the flow of charge. Magnetic fields exert
forces on moving charges, and so they exert forces on other magnets, all of which have
moving charges.
Right Hand Rule 1
The magnetic force on a moving charge is one of the most fundamental known. Magnetic force
is as important as the electrostatic or Coulomb force. Yet the magnetic force is more complex,
in both the number of factors that affects it and in its direction, than the relatively simple
Coulomb force. The magnitude of the magnetic force F on a charge q moving at a speed v in
a magnetic field of strength B is given by
F = qvB sin θ,

where θ is the angle between the directions of v and B. This force is often called the Lorentz
force. In fact, this is how we define the magnetic field strength B—in terms of the force on a
charged particle moving in a magnetic field. The SI unit for magnetic field strength B is called
the tesla (T) after the eccentric but brilliant inventor Nikola Tesla (1856–1943). To determine
how the tesla relates to other SI units, we solve F = qvB sin θ for B.
B=Fqvsinθ
Because sin θ is unitless, the tesla is1
1 T=1 N C⋅ m/s=1 NA⋅ m
(note that C/s = A). Another smaller unit, called the gauss (G), where 1 G = 10−4 T, is
sometimes used. The strongest permanent magnets have fields near 2 T; superconducting
electromagnets may attain 10 T or more. The Earth’s magnetic field on its surface is only about
5 × 10−5 T, or 0.5 G.
The direction of the magnetic force F is perpendicular to the plane formed by v and B, as
determined by the right hand rule 1 (or RHR-1), which is illustrated in Figure 1. RHR-1 states
that, to determine the direction of the magnetic force on a positive moving charge, you point
the thumb of the right hand in the direction of v, the fingers in the direction of B, and a
perpendicular to the palm points in the direction of F. One way to remember this is that there
is one velocity, and so the thumb represents it. There are many field lines, and so the fingers
represent them. The force is in the direction you would push with your palm. The force on a
negative charge is in exactly the opposite direction to that on a positive charge.

Figure 1. Magnetic fields exert forces on moving charges. This force is one of the most basic known. The
direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B and
follows right hand rule–1 (RHR-1) as shown. The magnitude of the force is proportional to q, v, B, and the
sine of the angle between v and B.
There is no magnetic force on static charges. However, there is a magnetic force on moving
charges. When charges are stationary, their electric fields do not affect magnets. But, when
charges move, they produce magnetic fields that exert forces on other magnets. When there
is relative motion, a connection between electric and magnetic fields emerges—each affects
the other.

Magnetic Forces on Moving Charges
The magnetic force on a free moving charge
is perpendicular to both the velocity of the
charge and the magnetic field with direction
given by the right hand rule. The force is
given by the charge times the vector
product of velocity and magnetic field.
If the velocity is perpendicular to the magnetic field then the force is given by the
simple product

Lorentz Force:
Lorentz force is the force exerted on a charged particle moving through both electric and
magnetic field.
F = qE + qv × B ……….(1)
where,
F = Lorentz Force
q = Charge on the Particle
E = Electric Field
B = Magnetic Field
v = Velocity of the Particle
In a vacuum where collisions between particles are not very frequent, a particle with charge
q, mass m, and velocity v perpendicular to a uniform magnetic field B (no E) moves in a circular
path with the radius
r = mv / qB ………..(2)
One can also deflect the trajectory of a charged particle with an electric field, although not into
a circular path. If the electric force on the particle is both equal and opposite to the magnetic
force, the net force on the particle will be zero. From Eq. (1), this will happen if
v=E / B ……….(3)
The motion of a charged particle in the electric and magnetic field
In case of motion of a charge in a magnetic field, the magnetic force is perpendicular to the
velocity of the particle. So no work is done and no change in the magnitude of the velocity is
produced (though the direction of momentum may be changed). We shall consider the motion

of a charged particle in a uniform magnetic field. First, consider the case of v perpendicular to
B.
The perpendicular force, q v × B, acts as a centripetal force and produces a circular motion
perpendicular to the magnetic field. If velocity has a component along B, this component
remains unchanged as the motion along the magnetic field will not be affected by the magnetic
field.
:
The motion in a plane perpendicular to B is as before a circular one, thereby producing a
helical motion. However, the electric field in y-direction imparts acceleration in that direction.
The particle, therefore, acquires velocity in the y-direction and resulting motion is a helical
motion.

The radius of each of the circular element and other periodic attributes like time period,
frequency and angular frequency are same as for the case of circular motion of charged
particle in perpendicular to magnetic field.
If there is a component of the velocity parallel to the magnetic field (denoted by v2), it will make
the particle move along both the field and the path of the particle would be a helical one. The
distance moved along the magnetic field in one rotation is called pitch p.
Ampere’s Law:
A useful law that relates the net magnetic field along a closed loop to the electric
current passing through the loop.
First discovered by André-Marie Ampère in 1826 .
The integral around a closed path of the component of the magnetic field tangent to
the direction of the path equals µ0 times the current intercepted by the area within the path

Thus the line integral (circulation) of the magnetic field around some arbitrary closed curve
is proportional to the total current enclosed by that curve.

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