GENERAL PHYSICS 2

Jiselle C. Dela Vega

Teacher II
 MELCs

❑ Identify the factors that affect the magnitude of the induced emf and the
magnitude and direction of the induced current (Faraday’s law)
STEM_GP12EMIVa-1
❑ Compare and contrast electrostatic electric field and non-
electrostatic/induced electric field STEM_GP12EMIVa-3
❑ Calculate the induced emf in a closed loop due to a time-varying magnetic
flux using Faraday’s law. STEM_GP12EMIVa-4
❑ Describe the direction of the induced electric field, magnetic field, and current
on a conducting/nonconducting loop using Lenz’s Law. STEM_GP12EMIVa-5.
❑ Compare and contrast alternating current (AC) and direct current (DC).
STEM_GP12EMIVb-6
Arrange the jumbled letters to form the word(s) to the given picture.

A coil of wire that acts as a

magnet when an electric
current flows through it.

SOLENOID
Arrange the jumbled letters to form the word(s) to the given picture.

the region around a

magnetic material or a
moving electric charge within
which the force of magnetism
acts.
MAGNETIC FIELD
Arrange the jumbled letters to form the word(s) to the given picture.

any material capable of

attracting iron and producing
a magnetic field outside itself

MAGNETS
Arrange the jumbled letters to form the word(s) to the given picture.

this device is used on

electrical circuits to know and
measure the intensity and
direction of electrical current.

GALVANOMETER
Arrange the jumbled letters to form the word(s) to the given picture.

a measurement of
the total magnetic
field which passes
through a given area

number of magnetic field lines

passing through a given closed
MAGNETIC FLUX surface
 REVIEW
ELECTRIC FIELD
Stationary electric charges produce _____________ and moving electric
MAGNETIC FIELD
charges (that is, electric current) produce _______________

Hans Christian Oersted discovered that electric current creates a magnetic field
around it in 1820.

changing magnetic flux produces electric field or induces electric

current
 MICHAEL FARADAY
He did experiments regarding the reverse relationship between
magnetism and electricity, that is, the creation of an electric current
using a magnetic field.

led to the development of the electric motor, electric generator,

and the transformer

application of the concept Magnetic Induction

 FARADAY’S
MAGNETIC
INDUCTION
Is it possible to produce an
electric current using only
wires and no battery?
❑ It is also possible to induce current in a circuit without the
use of a battery or an electrical power supply.
❑ Just as a magnetic field can be formed by a current in a
circuit , a current can be formed by moving a portion of a
closed electric circuit through an external magnetic
field
ELECTROMAGNETIC INDUCTION

❑In 1831, two physicists, Michael Faraday in England and Joseph

Henry in the United States, independently discovered that
magnetism could produce an electric current in a wire

❑Their discovery was to change the world by making electricity so

commonplace that it would power industries by day and light
up cities by night.
 ELECTROMAGNETIC INDUCTION
❑The process of inducing a current in a circuit with a changing
magnetic field is called Electromagnetic Induction or Magnetic
Induction.

✓ A current is set up even though no

batteries are present in the circuit.
✓ We call such a current an induced
current and say that it is produced
by an induced emf.
FARADAY’S
EXPERIMENT
MAGNETIC FLUX
❑The magnetic flux (often denoted Φ or ΦB) through a surface is the
component of the magnetic field passing through that surface
❑magnetic flux through some surface is proportional to the number of field
lines passing through that surface. The magnetic flux passing through a
surface of vector area A is

❑ ΦB is the magnetic flux(having the unit Weber ,Wb),

❑ B is the magnitude of the magnetic field (having the unit of Tesla, T (Newton/Ampere-meter (N/Am)
but when calculating induced emf we use 1 T = 1 volt-sec/meter2 (Vs/m2),
❑ A is the area of the surface(m2), and
❑ θ is the angle between the magnetic field lines and the normal (perpendicular) to A.
INDUCED EMF
❑The apparatus used by Faraday
to demonstrate that magnetic
fields can create currents. When
the switch is closed, a magnetic
field is produced in the coil on
the top part of the iron ring and
transmitted (or guided) to the
coil on the bottom part of the
ring. The galvanometer is used
to detect any current induced in
a separate coil on the bottom.

Faraday's iron ring apparatus

 It was found that each time the switch is closed, the galvanometer detects a
current in one direction in the coil on the bottom. Each time the switch is opened,
the galvanometer detects a current in the opposite direction. Interestingly, if the
switch remains closed or open for any length of time, there is no current through
the galvanometer. Closing and opening the switch induces the current.
- What creates the current in the apparatus?

- It is the change in magnetic field that creates the current. More basic than the
current that flows is the electromotive force (EMF) that causes it. The current is
a result of an EMF induced by a changing magnetic field, whether or not there is
a path for current to flow.

Image By Wikipedia
Faraday's iron ring apparatus
FARADAY’S LAW OF INDUCTION
❑ Faraday observed that current flows in the coil, only when there is a relative
motion between the coil and the magnet

Faraday’s law of induction is a basic law of electromagnetism that predicts how

a magnetic field will interact with an electric circuit to produce an electromotive
force (EMF). It is the fundamental operating principle of transformers,
inductors, and many types of electrical motors, generators, and
solenoids.
Considering the magnetic flux through a wire loop, Faraday
asked what happened if you placed a magnet close to the loop
and let it sit there. Would a current appear in the presence of
the magnet?
❑ He carried out the experiment and found that there was
no current in the loop.
❑ However, if you move the magnet away, then for a brief
instant a current appears. If you move it back, then a
current appears.
Faraday’s experiments showed that the emf induced by a
change in magnetic flux depends on only a few factors.

1. emf is directly proportional to the change in flux Δ.

2. emf is greatest when the change in time, Δt, is smallest
3. if a coil has N turns, an emf that will be produced is N times
greater than for a single coil
FARADAY’S LAW OF MAGNETIC INDUCTION
❑ What Faraday found is there is an induced current (and
therefore induced voltage) only when the magnetic flux
changes over time.
APPLICATION OF ELECTROMAGNETIC
INDUCTION:
TRUE

TRUE

TRUE

TRUE

TRUE
The equation for the emf induced by a change
in magnetic flux is known as Faraday’s Law.
LENZ’S LAW

❑ Faraday’s law indicates that the induced emf

and the change in flux have opposite algebraic
signs. This has a physical interpretation that
has come to be known as Lenz’s Law.
❑ developed by Heinrich Friedrich Emil Lenz, in

1834, a Russian physicist of Baltic German

family
LENZ’S LAW

❑ The minus in the equation of Faraday’s law

means that the emf creates a current I and
magnetic field B that oppose the change in
flux ΔΦ
❑ states that the induced current in a loop is in

the direction that creates a magnetic field that

opposes the change in magnetic flux through
the area enclosed by the loop.
 LENZ’S LAW EXPLAINED

Now according to Lenz’s law, this magnetic field created will oppose its own or
opposes the increase in flux through the coil and this is possible only if the
approaching coil side attains north polarity, as we know similar poles repel each
other. Once we know the magnetic polarity of the coil side, we can easily determine
the direction of the induced current by applying the right-hand rule. In this
case, the current flows in the counterclockwise direction.
 LENZ’S LAW EXPLAINED

Now according to Lenz’s law, this magnetic field created will oppose
its own or opposes the decrease in flux through the coil and this is
possible only if the approaching coil side attains south polarity, as
we know dissimilar poles attract each other. Following the right-hand
rule, the current flows in a clockwise direction
LENZ’S LAW EXPLAINED
Determine the direction of the current
induced in the coil for each situation:

CCW
Determine the direction of the current
induced in the coil for each situation:

CCW
 Determine the direction of the current
induced in the coil for each situation:

CW
Determine the direction of the current
induced in the coil for each situation:

CCW
GENERAL PHYSICS 2
 MELCS
• Relate the properties of EM wave (wavelength, frequency, speed) and
the properties of vacuum and optical medium (permittivity,
permeability, and index of refraction) STEM_GP12OPTIVb-12
• Explain the conditions for total internal reflection
STEM_GP12OPTIVb-14
• Explain the phenomenon of dispersion by relating to Snell’s Law
STEM_GP12OPTIVb-16
• Calculate the intensity of the transmitted light after passing through a
series of polarizers applying Malus’s Law STEM_GP12OPTIVc-18
 WHAT IS AN ELECTROMAGNETIC WAVE?
• Electromagnetic waves are produced once
electrically charged particles accelerate and
interact with other particles.
• created by the interaction of changing electric
and magnetic fields with directions that are 90
degrees apart. The directions of these fields
are also perpendicular to the energy and wave
propagation directions. (transverse wave)
• does not require a medium to propagate
because it consists solely of oscillating electric
and magnetic fields. As a result, they can
travel across a vacuum.
 WHAT IS AN ELECTROMAGNETIC
WAVE?
• electromagnetic wave, which travels at the speed of light
and contains photons as its principal elements
• electromagnetic waves include microwaves, infrared, radio
waves, X-rays, ultraviolet rays, visible light, and gamma
rays.
• Electricity can be static, like the energy that can make
your hair stand on end. Magnetism can also be static, as
it is in a refrigerator magnet.

• A changing magnetic field will induce a changing electric

field and vice-versa the two are linked. These changing
fields form electromagnetic waves.
 FREQUENCY
WAVELENGTH
MAGNETISM
ELECTROMAGNETISM
ELECTROMAGNETIC SPECTRUM
 ELECTROMAGNETIC WAVES
• are transverse waves with a wide range of properties and
uses.
• Some of the waves are also hazardous to human body
tissues.
• Their vibrations or oscillations are changes in electrical and
magnetic fields at right angles to the direction of wave travel.
• Electromagnetic waves travel at 300,000,000 meters per
second (m/s) through a vacuum.
All electromagnetic waves:
• transfer energy from the source of the waves to an absorber.
• can travel through a vacuum such as in space.
• all travel at the same velocity through a vacuum.
 Red, the longest of the wavelengths, measures
around 700 nanometers; yellow is around 600
nanometers; and violet, the shortest, is around 400
nanometers in length.
• The terms of light, electromagnetic waves, and radiation all
refer to the same physical phenomenon: electromagnetic
energy. This energy can be described by frequency,
wavelength, or energy.
• Radio and microwaves are usually described in terms of
frequency (Hertz),
• infrared and visible light in terms of wavelength (meters),
• and x-rays and gamma rays in terms of energy (electron
volts).
FREQUENCY
• The number of crests that pass a given point within one
second
• One wave – one cycle – per second is called a Hertz(Hz),
after Heinrich Hertz who established the existence of radio
waves.
• A wave with two cycles that pass a point in one second
has a frequency of 2 Hz.
WAVELENGTH
• Electromagnetic waves have crests and troughs similar to those
of ocean waves.
• The distance between crests is the wavelength.
• The shortest wavelengths are just fractions of the size of an
atom,
• longest wavelengths scientists currently study can be larger
than the diameter of our planet.
ENERGY
• An electromagnetic wave can also be described in terms of its
energy – in units of measure called electron volts (eV).
• An electron volt is the amount of kinetic energy needed to
move an electron through one-volt potential.
• Moving along the spectrum from long to short wavelengths,
energy increases as the wavelength shortens.
MAXWELL’S SYNTHESIS OF ELECTRICITY,
MAGNETISM AND OPTICS
• Scottish physicist named James Clerk Maxwell published a
theory that accounted for the physical origins of light.
• One prediction that came from Maxwell's equations was that: a
charge moving back and forth in a periodic fashion would create
an oscillating electric field. This electric field would then set up
a periodically changing magnetic field, which in turn would
cause the original electric field to continue its oscillation, and
so on.
• This mutual vibration allowed the electric and magnetic fields
to travel through space in the form of an "electromagnetic
wave,"
• Maxwell's electromagnetic waves could have a range of
wavelengths and corresponding frequencies
• This range of wavelengths is now known as the
"electromagnetic spectrum."
• Maxwell's theory also predicted that all the waves in the
spectrum travel at a characteristic speed of approximately
300,000,000 meters per second.
• Maxwell was able to calculate this speed from his equations:
• Maxwell's calculation of the speed of an electromagnetic wave included two
important constants: the permittivity and permeability of free space.
• The permittivity of free space is also known as the "electric constant" and describes
the strength of the electrical force between two charged particles in a vacuum.
• The permeability of free space is the magnetic analogue of the electric constant. It
describes the strength of the magnetic force on an object in a magnetic field.
• Thus, the speed of an electromagnetic wave comes directly from a fundamental
consideration of electricity and magnetism.
 electromagnetic radiation
electric magnetic

3.0 x10^8
 transverse

vacuum
spectrum
frequency wavelength

permeability permittivity

electricity magnetism
• A light wave does not just stop when it reaches the
end of the medium. Rather, the light wave
undergoes certain behaviors when it encounters
the end of the medium - such behaviors include
reflection, transmission/refraction, and diffraction.
•Alaw states that when a light ray reflects off
a surface, the angle of incidence is equal to
the angle of reflection. LAW OF REFLECTION
•A law states that when a light ray is transmitted into a
new medium, the relationship between the angle of
incidence and the angle of refraction is given by the
following equation ni•sine(Θi) = nr • sine(Θr)
SNELL’S LAW
SNELL’S LAW
•A light wave, like any wave, is an energy-transport
phenomenon.
• A light wave transports energy from one location to another.
When a light wave strikes a boundary between two distinct
media, a portion of the energy will be transmitted into the
new medium and a portion of the energy will be reflected off
the boundary and stay within the original medium.
• Reflection of a light wave involves the
bouncing of a light wave off the boundary,
while
• refraction of a light wave involves the bending
of the path of a light wave upon crossing a
boundary and entering a new medium.
• The fundamental law that governs the reflection of light is
called the law of reflection.
• Whether the light is reflecting off a rough surface or a smooth
surface, a curved surface or a planar surface, the light ray
follows the law of reflection.
• The law of reflection states that “When a light ray reflects off
a surface, the angle of incidence is equal to the angle of
reflection.”
• The fundamental law that governs the refraction of light
is Snell's Law.
• Snell's Law states that “When a light ray is transmitted
into a new medium, the relationship between the angle
of incidence (Θi) and the angle of refraction (Θr) is given
by the following equation: ni • sine(Θi) = nr • sine(Θr)
• ni and nr - the indices of refraction of the incident and the
refractive medium
 A ray of light passing from a dense medium into a rear medium refracts and bends away from the
normal line. The angle of refraction is greater than the angle of incidence. When the angle of refraction
is equal to 90 degrees, we get a critical angle. In this case, the angle of incidents is equal to the critical
angle but when the angle of incidence becomes greater than the critical angle then, the refracted ray
does not enter the rear medium rather, it is reflected in the same medium. This is what we call the
TOTAL INTERNAL REFLECTION.
 Many optical instruments use the principle of total
internal reflection. Total internal reflection is used in
instrument such as fiber optic, binoculars, and periscope.
POLARIZATION
(MALUS’ LAW)
❑ A light wave that is vibrating in more than one plane is
referred to as unpolarized light.
❑ Examples: (Natural Light) Light emitted by the sun, by a
lamp in the classroom, or by a candle flame
❑ Such light waves are created by electric charges that
vibrate in a variety of directions, thus creating an
electromagnetic wave that vibrates in a variety of
directions.
• It is possible to transform unpolarized
light into polarized light
• Polarized light waves are light waves in which
the vibrations occur in a single plane.
• processof transforming unpolarized light into
polarized light is known as polarization.
APPLICATION OF MALUS’ LAW
• sunglasses,
• windowpanes,
• sometimes photographic and 3d movie cameras
• Polarization is used in sunglasses to reduce the glare
 HOW DOES A POLARIZER WORK?
• Polarizers are usually made out of
oblong shaped molecules, all
aligned in the same direction.
• It turns out that if the polarization of the
incident beam is the same as
alignment orientation, then the light is
most likely to be absorbed.
• If the polarization is perpendicular to
the long axis of molecules, then it is
transmitted almost entirely and that
direction is the axis of the polarizer.
• The exact value can be determined
thanks to the Malus law.
 MALUS’ AW

• Étienne-Louis Malus, French physicist who

discovered that light, when reflected,
becomes partially plane polarized; i.e., its
rays vibrate in the same plane.
• His observation led to a better
understanding of the propagation of light.
When light falls on a polarizer, the transmitted light
gets polarized.
The polarized light falling on another Polaroid, called
analyzer, transmits light depending on the
orientation of its axis with the polarizer.

The intensity of light transmitted through the

analyzer is given by Malus' law
MALUS’ LAW

• statesthat the intensity of a plane-polarized light

that passes through an analyzer varies as the
square of the cosine of the angle between the
plane of the polarizer and the transmission axes of
the analyzer.
MALUS LAW FORMULA

• The intensity (I) of polarized light after passing through

a polarizing filter is usually measured in 𝑊/𝑚2 . The light
intensity, which passes through the ideal polarizer can be
calculated as:

• I = I0 cos2 θ Equation

• Where, I0 is the initial intensity of light

• θ is the angle between the direction of polarization and the
axis of the filter.
Example: Intensity of Light Changes under rotation.
Let us say that you want to check how the intensity of polarized light
changes, while you rotate your polarizer.
1. Choose a few different values of the axis of polarizer orientation with
respect to the polarization of incident rays, e.g. θ₁=20°, θ₂=45°, θ₃=70°,
2. Determine cosθ of these angles, which
are 0.939, 0.707, 0.342 respectively,
3. Find squares of this values: 0.883, 0.5, 0.117,
4. Multiply them by the initial intensity, say I₀=5 W/m²: I₁=4.415 W/m², I₂=2.5
W/m², I₃=0.585 W/m²...
You can always express obtained results as the percentages of initial
intensity.
1. Unpolarized light with intensity I0 passes through a polarizer and then a
second polarizing filter (analyzer) with an angle of 30 degrees relative to the
first one. What is the intensity of the light as it passes through each filter in
terms of I0?
1. Unpolarized light with intensity I0 passes through a polarizer and then a second polarizing filter
(analyzer) with an angle of 30 degrees relative to the first one. What is the intensity of the light as it
passes through each filter in terms of I0?
TRY THIS!

Unpolarized light of intensity 1.2 watts/m^2 is incident

on a polarizer.
(a) What is the intensity of the light leaving the
polarizer?
(b) If an analyzer is set at 60 degrees with respect to
the polarizer, what is the intensity of light leaving
the analyzer?
Given:
Initial intensity of the unpolarized light = 1.2 watts/m^2
a. Upon leaving the polarizer, the intensity is reduced to ½
½ (1.2 watts/m^2)
= 0.6 watt/m^2
a. 𝐼 = 𝐼0 𝑐𝑜𝑠 2 θ
= (0.6𝑤𝑎𝑡𝑡𝑠
𝑚2
)𝑐𝑜𝑠 2 600

𝒘𝒂𝒕𝒕𝒔
I = 0.15
𝒎𝟐