1.

Properties of Electric Charges

 Additivity of Electric Charge

Let us consider a system of charges containing three point charges with magnitude q1, q2, and q3. In such a system, the total charge of the system can be
obtained by algebraically adding the three charges.

These charges have magnitude but no direction, are scalar quantities, and are treated like real numbers during conducting any operation. For a system
containing n particles, the total charge of the system can be written as,

We note that the charge can either be positive or negative and the operation takes the sign of the charge into consideration.

 Conservation of Electric Charge

According to the principle of conservation of charges, the charges are neither created nor destroyed; they are only transferred from one body to the other.

 Quantization of Electric Charge

According to the principle of quantization of electric charge, all the free charges are integral multiples of a basic predefined unit which we denote by e. Thus, the
charge possessed by a system can be given as,

2. The Nature of Light

Light is a transverse, electromagnetic wave that can be seen by the typical human. The wave nature of light was first
illustrated through experiments on diffraction and interference. Like all electromagnetic waves, light can travel through
a vacuum. In physics, there are two theories by which light can be defined: the first theory defines light as particles and
the second theory as waves. When considering measurement equipment such as spectro[radio]meters, which
measure light in wavelengths, the second theory is the most suitable to explain light.

3. Dual Nature of Light

Light consists of dual nature which means sometimes it behaves like a particle (known as photon), which explains how
the light travels in straight lines. Sometimes light behaves as the wave, which explains how light bends (or diffract)
around an object.

4. Magnetic Flux

Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. It
provides the measurement of the total magnetic field that passes through a given surface area. Here,
the area under consideration can be of any size and under any orientation with respect to the direction
of the magnetic field.

ϕB=B.A=BAcosΘ
 5. The Ray Approximation in Ray Optics
One approximation that geometric optics makes is that the waves (rays) travel in straight lines until they hit a surface.
When the ray encounters a surface it can either bounce back (reflect) or bend (refract) but then continues to travel in a
straight line.

6. Lenz's Law

The induced electromotive force with different polarities induces a current whose magnetic field
opposes the change in magnetic flux through the loop in order to ensure that original flux is
maintained through the loop when current flows in it.

Emf=−N(Δϕ/Δt)
7. Analysis Model: Particle in a Electric Field
In an electric field a charged particle, or charged object, experiences a force. If the forces acting on any object are
unbalanced, it will cause the object to accelerate. If two objects with the same charge are brought towards each other
the force produced will be repulsive, it will push them apart. The electric field will exert a force that accelerates
the charged particle. ... This is the direction that the electric field will cause a positive charge to accelerate. If a
positive charge is moving in the same direction as the electric field vector the particle's velocity will increase.

8. Reflection of Light
The reflection of light can be roughly categorized into two types of reflection. Specular reflection is defined as light
reflected from a smooth surface at a definite angle, whereas diffuse reflection is produced by rough surfaces that tend
to reflect light in all directions. Consider a light-ray incident on a plane mirror, the law of reflection states that the
incident ray, the reflected ray, and the normal to the surface of the mirror all lie in the same plane. The angle
of reflection is equal to the angle of incidence. Both angles are measured with respect to the normal to the mirror.

9. Electric Field Lines

An electric field line is, in general, a curve drawn in such a way that the tangent to it at each point is in
the direction of the net field at that point. An arrow on the curve is obviously necessary to specify
the direction of electric field from the two possible directions indicated by a tangent to the curve. A
field line is a space curve, i.e., a curve in three dimensions.

The field lines follow some important general properties:

(i) Field lines start from positive charges and end at negative charges. If there is a single charge, they
may start or end at infinity.
(ii) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks.
(iii) Two field lines can never cross each other. (If they did,the field at the point of intersection will not
have a unique direction, which is absurd.)
(iv) Electrostatic field lines do not form any closed loops. The field lines follow some important general
properties:
(i) Field lines start from positive charges and end at negative charges. If there is a single charge, they
may start or end at infinity.
(ii) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks.
(iii) Two field lines can never cross each other. (If they did,the field at the point of intersection will not
have a unique direction, which is absurd.)
(iv) Electrostatic field lines do not form any closed loops.

10. Refraction of Light

Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent
substance into another. This bending by refraction makes it possible for us to have lenses, magnifying glasses, prisms
and rainbows. Refraction is the bending of a wave when it passes from one medium to another. The
bending is caused due to the differences in density between the two substances.

11. Motion of a Charged Particle in a Uniform Electric Field

A uniform electric field is a field in which the value of the field strength remains the same at all points. In a uniform
electric field, as the field strength does not change and the field lines tend to be parallel and equidistant to each other.

12. The Index of Refraction

The index of refraction, n, is the ratio of the speed of light in a vacuum, c, to the speed of light in a medium, c': n=c/c’

Refractive index, also called index of refraction, measure of the bending of a ray of light when passing from one medium
into another. ... Refractive index is also equal to the velocity of light c of a given wavelength in empty space divided by
its velocity v in a substance, or n = c/v.

13. Snell's Law of Refraction

Snell's Law, which can be stated as. nA Sinθ A = nB Sinθ B. predicts how the ray will change direction as it passes from
one medium into another, or as it is reflected from the interface between two media.

14. Huygens's Principle

Huygens' principle states that every point on a wave front may be considered as a source of secondary waves. The word
interference is used to describe the superposition of two waves, whereas diffraction is interference produced by several
waves.

15. Mass Spectrometer

The mass spectrometer is an instrument which can measure the masses and relative concentrations of atoms and
molecules. It makes use of the basic magnetic force on a moving charged particle. Mass spectrometry is an analytical
tool useful for measuring the mass-to-charge ratio (m/z) of one or more molecules present in a sample. These
measurements can often be used to calculate the exact molecular weight of the sample components as well.

16. Faraday's Law of Induction

Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No
matter how the change is produced, the voltage will be generated. The change could be produced by changing the
magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic
field, rotating the coil relative to the magnet, etc.

17. Dispersion
Dispersion is defined as the spreading of white light into its full spectrum of wavelengths. More
technically, dispersion occurs whenever the propagation of light depends on wavelength. The separation of
visible light into its different colors is known as dispersion. It was mentioned in the Light and Color unit that each color is
characteristic of a distinct wave frequency; and different frequencies of light waves will bend varying amounts upon
passage through a prism. When the white light passes through some transparent material such as glass prism, it splits
into its seven constituent colors. This phenomenon of splitting of white light is known as dispersion of light.

18. Electric Potential

Electric potential, the amount of work needed to move a unit charge from a reference point to a specific point against
an electric field

V = k × [q/r]

19. Total Internal Reflection. Critical Angle

The phenomenon which occurs when the light rays travel from a more optically denser medium to a
less optically denser medium.

Critical angle, in optics, the greatest angle at which a ray of light, travelling in one transparent medium, can strike the
boundary between that medium and a second of lower refractive index without being totally reflected within the first
medium.

20. Notation for Mirrors and Lenses

A lens is a transparent device with two curved surfaces, usually made of glass or plastic, that uses refraction to form an
image of an object. Mirrors, which have curved surfaces designed to reflect rays, also form images. The position to
which the rays converge to or diverge from is the image. Difference Between Lens and Mirror. The lens is a material
made of glass or plastic bounded by two surfaces. It can either be curved at one side or both sides. The mirror implies a
glossy surface at one end and produces an image of an object by reflection.
 21. . Balmer's generalized formula

22. Combinations of Capacitors

When several capacitors are connected in a series combination, the reciprocal of the equivalent capacitance is the sum
of the reciprocals of the individual capacitances. When several capacitors are connected in a parallel combination, the
equivalent capacitance is the sum of the individual capacitances.

23. Images Formed by Flat Mirrors. Lateral Magnification

The image formed by a plane mirror is always virtual (meaning that the light rays do not actually come from the image),
upright, and of the same shape and size as the object it is reflecting. A virtual image is a copy of an object formed at the
location from which the light rays appear to come. Lateral magnification is defined as the ratio of image height to object
height in an optical system.

24. Electric Current

An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or
space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. 1 ampere =
1 coulomb / 1 second

25. Spherical Mirrors

A spherical mirror is a mirror that has the shape of a piece cut out of a spherical surface. There are two types
of spherical mirrors: concave and convex mirror.

Image location − Image is formed between center of curvature and focus. Size − Diminished. Nature − As image is
formed by actual intersection of rays, hence it is real. Orientation − Image is inverted.

26. Image Formed by a Concave Mirror

For concave mirrors, when the object is outside C, the image will be between C and F and the image will be inverted and
diminished (smaller than the object). ... For concave mirrors, when the object is between F and the mirror,
the image will be behind the mirror and will be enlarged and upright. Concave mirrors form both real and virtual images.
When the concave mirror is placed very close to the object, a virtual and magnified image is obtained and if we increase
the distance between the object and the mirror, the size of the image reduces and real images are formed.
 27. Differences Between Electric and Magnetic Fields
Difference Between Electric Field vs Magnetic Field

Electric Field Magnetic Field

It creates an electric charge in surrounding Creates an electric charge around moving magnets

Measured as newton per coulomb, volt per meter Measured as gauss or tesla

Proportional for the electric charge Proportional to the speed of electric charge

Are perpendicular to the magnetic field Are perpendicular to the electric field

An electric field is measured using an electrometer The magnetic field is measured using the magnetometer

28. Mirror equation

It is an equation relating object distance and image distance with focal length is known as a mirror
equation. It is also known as a mirror formula.

 u is the Object distance

 v is the Image distance
 f is the Focal Length given by f=R/2
 R is the radius of curvature of the spherical mirror

29. Resistors in Series and Parallel

In a series circuit, the output current of the first resistor flows into the input of the second resistor; therefore, the
current is the same in each resistor. In a parallel circuit, all of the resistor leads on one side of the resistors are
connected together and all the leads on the other side are connected together.

30. Balmer series

The Balmer series is the name given to a series of spectral emission lines of the hydrogen atom that result from electron
transitions from higher levels down to the energy level with principal quantum number 2. These lines are emitted when
the electron in the hydrogen atom transitions from the n = 3 or greater orbital down to the n = 2 orbital. The
wavelengths of these lines are given by 1/λ = RH (1/4 − 1/n2), where λ is the wavelength, RH is the Rydberg constant, and
n is the level of the original orbital.

31. Thin Lens Equation

32. Symbols for Circuit Diagrams

33. Young's Double-Slit Experiment

34. Conditions for Interference

 When waves come together they can interfere constructively or destructively. To set up a stable
and clear interference pattern, two conditions must be met:
 The sources of the waves must be coherent, which means they emit identical waves with a
constant phase difference.
 The waves should be monochromatic - they should be of a single wavelength.
 35. Series of spectral lines for atoms
The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given
by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy
levels in an atom.

36. Interference Equations

37. Hydrogen electron's velocity in the bohr model

According to this equation the angular momentum of the electron relative to the nucleus is quantized. ... Hence
the velocity of the electron in the first Bohr orbit of the hydrogen atom is 2.18×106m/sec.

38. Resistors in Series and Parallel

39. Rydberg constant
describing the wavelengths or frequencies of light in various series of related spectral lines, most notably those emitted

by hydrogen atoms in the Balmer 10 973 731.6 m -1

40. Kirchhoff s Rules

Kirchhoff's first rule—the junction rule: The sum of all currents entering a junction must equal the sum of all currents
leaving the junction. Kirchhoff's second rule—the loop rule: The algebraic sum of changes in potential around any closed
circuit path (loop) must be zero.

41. Fraunhofer Diffraction

Fraunhofer diffraction is the type of diffraction that occurs in the limit of small Fresnel number . In Fraunhofer
diffraction, the diffraction pattern is independent of the distance to the screen, depending only on the angles to the
screen from the aperture.

42. Symbols for Circuit Diagrams

43. Rutherford's Thin Foil Experiment
The Rutherford Gold Foil experiment shot minute particles at a thin sheet of gold. It was found that a small percentage
of the particles were deflected, while a majority passed through the sheet. This caused Rutherford to conclude that the
mass of an atom was concentrated at its center.

44. Electromotive Force

Electromotive force is defined as the electric potential produced by either electrochemical cell or by
changing the magnetic field. EMF is the commonly used acronym for electromotive force.

Ε = V + Ir

Where,

 V is the voltage of the cell

 I is the current across the circuit
 r is the internal resistance of the cell
 ε is the electromotive force
45. Models of the Atom
 Dalton model (Billiard ball model)
 Thomson model (Plum pudding model)
 Lewis model (Cubical atom model)
 Nagaoka model (Saturnian model)
 Rutherford model (Planetary model)
 Bohr model (Rutherford–Bohr model)
 Bohr–Sommerfeld model (Refined Bohr model)
 Gryziński model (Free-fall model)
46. Differences Between Electric and Magnetic Fields
47. Bohr's Postulates

Postulates of Bohr’s Model of an Atom

 In an atom, electrons (negatively charged) revolve around the positively charged nucleus in a
definite circular path called orbits or shells.
 Each orbit or shell has a fixed energy and these circular orbits are known as orbital shells.
 The energy levels are represented by an integer (n=1, 2, 3…) known as the quantum number.
This range of quantum number starts from nucleus side with n=1 having the lowest energy level.
The orbits n=1, 2, 3, 4… are assigned as K, L, M, N…. shells and when an electron attains the
lowest energy level, it is said to be in the ground state.
  The electrons in an atom move from a lower energy level to a higher energy level by gaining the
required energy and an electron moves from a higher energy level to lower energy level by
losing energy.
48. Bohr's second postulate
49. Electric Flux
50. Bohr's third postulate
51. Determintion of orbital radius in the bohr model

0.52
The radius of the first Bohr orbit of hydrogen atom is 0.52.

52. Hydrogen energy levels in the bohr model

The Bohr model is used to describe the structure of hydrogen energy levels. ... The amount of energy in each level is
reported in eV, and the maxiumum energy is the ionization energy of 13.598eV.

53. Coulomb's law

Coulomb's law, or Coulomb's inverse-square law, is an experimental law of physics that quantifies the amount of force
between two stationary, electrically charged particles. The electric force between charged bodies at rest is
conventionally called electrostatic force or Coulomb force.