Studied by 9 people
Chapter 1
Electric Charges and Field
Coulomb’s Law
The electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them
Electric Flux
The number of electric field lines passing normally in a given area
Gauss Law
The total electric flux over a closed surface equals 1/εo times the net charge enclosed by the surface
Chapter 2
Electrostatic Potential and Capacitance
Electric Potential
The work done to bring a unit positive charge from infinity to a point against electrostatic force
Equipotential surfaces
Surface in which all points have same potential
Electrostatics of Conductors
Inside a conductor, the electrostatic field is zero since all the charges reside only on the surface
At the surface of a charged conductor (E = σ/εo), the electrostatic field must be normal to the surface at every point
Under static conditions, all the charges in a conductor lie on the surface
The electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface
Inside a cavity, the electric field is zero and protected from the external electric field. This is known as electrostatic shielding
Dielectrics
Insulating materials that have bound charges.
Two types:
Polar molecule: +ve and -ve charged centres don’t coincide; permanent dipole moment. Eg: HCl
Non-polar molecule: +ve and -ve charge centres coincide; induced dipole moment. Eg: H2, O2, CO2, CH4
Polarisation
The phenomenon in which a polar molecule orients itself along the direction of the external electric field or the non-polar molecules become temporary dipoles in presence of an external electric field
Chapter 3
Current Electricity
Ohm’s Law
The current flowing through a conductor is directly proportional to the potential difference across it when the temperature is constant
Limitations of Ohm’s Law
Does not hold good for all materials. Devices which do not obey Ohm’s law are called non-ohmic or non-linear devices
Temperature Dependence on Resistivity
For conductors: T increases; ρ increases
For semiconductors/insulators: T increases; ρ decreases
Metals have low resistivity and α is +ve and high
Nichrome has higher resistivity than metals and α is positive but low. Nichrome is used as a heating element since it has high resistivity
Manganin has higher resistance than metals but α is 0 and is used to make standard resistors
Semiconductors have high resistivity but α is -ve
Kirchoff’s Laws
First Law (Current Law): The sum of all the currents entering the junction is equal to the sum of the currents leaving the junction
Second Law (Voltage Law): The algebraic sum of the change in the potential for a closed loop involving resistors and cells in that group is zero
Chapter 4
Moving Charges and Magnetism
Biot Savart’s Law
The magnetic field due to a small current carrying element is directly proportional to:
Current element
sine of angle between the element and the point
and inversely proportional to:
Square of the distance between the element and the point
Ampere’s Circuital Law
The closed integral of magnetic flux over a loop equals μo times the current enclosed by the loop
Path of Charge
θ = 90o : circle
θ = 0o or 180o : straight line
θ ≠ 0o or 90o or 180o : helical
1 Ampere
1 Ampere is the current passing through two parallel wires which are separated by 1m and they experience a force 2 × 10-7N/m
Chapter 5
Magnetism and Matter
Properties of Bar Magnets
Has 2 equal and opposite poles
If a magnetic is cut into two pieces, they split into two magnets with each having its own north and south pole
There is no magnetic monopole
When a bar magnet is cut laterally, pole strength decreases and when it is cur transversely, pole strength remains same
Magnetic Field Lines
Imaginary lines that represent the magnetic field around a magnet
Properties of Magnetic Field Lines
Form continuous curves that originate at the north pole and end at the south pole outside. Inside, they go from south to north
They never cross each other
They are closer together in areas of stronger magnetic field and spread out in areas of weaker magnetic field
The density of field lines at a point is directly proportional to the strength of the magnetic field at that point
If magnetic field lines are parallel - uniform
The direction of the magnetic field is given by the tangent to the field lines at that point
Gauss Law for Magnetism
The closed integral of magnetic flux over a surface is zero
Diamagnetic Materials
Exhibit negative magnetism i.e align themselves opposite to the aligned magnetic field
Have no unpaired electrons
Negative susceptibility
Relative permeability less than 1
When freely placed in an external magnetic field, it goes from a stronger to a weaker region
When not allowed to move in an external magnetic field, field lines expel out of it
They are weakly repelled in the presence of an external field
Superconducting materials are diamagnetic and hence expel all magnetic field lines out of it
Ex: Bismouth, Pb, Cu, N2, Si, H2O, NaCl
Paramagnetic Materials
In the presence of an external field, the molecules align themselves in the direction of the field
Have unpaired electron(s)
Positive susceptibility
Relative Permeability greater than 1
When freely placed in an external magnetic field, it goes from a weaker to a stronger regions
They are weakly attracted in the presence of an external field
As the temperature increases, the molecules have thermal agitation so the net magnetic moment decreases. Hence the susceptibility of a paramagnet depends on temperature (inversely proportional)
Eg: Al, Na, Ca, O2, CuCl2
Ferromagnetic Materials
They are paramagnetic and form domains
Domains: groups of atoms/molecules that behave as a single unit
The susceptibility of ferro magnets is very high
Relative Permeability is a lot greater than 1
As temperature increases the domain will break and ferro magnets will become para magnets
Ferro magnets can be classified as:
Hard: Retain magnetic property even after removing from an external field
Eg: Alnico, loadstone
Soft: Does not retain magnetic property
Eg: Fe, Ni, Co, Gadolinium
Chapter 6
Electromagnetic Induction
Faraday’s Law of Induction
The induced emf developed is directly proportional to the rate of change of magnetic flux linked with the closed circuit
Lenz’s Law
Induced current always flows in a direction that opposes the rate of change of flux.
It is based in conservatioj of energy
Self Inductance and Mutual Inductance
The phenomenon in which rate if change of current in a coil creates induced EMF in the same coil/in another coil
1 Henry
Self: 1 henry is the self inductance of a coil which creates 1 Webber of magnetic flux when 1A current is passed through it
Mutual: 1 henry is the mutual inductance between two coils if 1A current passing through 1 coil creates a magnetic flux of 1 Wb in another coil
Chapter 7
Alternating Current
Phasor Diagrams
see cw
Wattless Current
In case of a pure inductor or capacitor, the average power dissipated over a complete cycle is zero. Thus, the current flowing through it is known as wattless current
Energy Loss in Transformers
Flux loss:
Cause: Flux created in primary coil is not completely linked with secondary coil
Minimisation: Keep the coils together
Heat Loss:
Cause: Heat loss in primary and secondary bindings due to resistance
Minimsation: Thick wires can be used
Eddy Current Loss:
Cause: Induced current in the core causes heat loss
Minimsation: Using laminated cores
Hysterisis Loss:
Cause: Repeated magnetisation and demagnetisation of the core created energy loss
Minimsation: Using materials with less hysterisis loss: Ex: Soft iron
Chapter 8
Electromagnetic Waves
Displacement Current
(Differentiate between conduction current and displacement current)
Maxwell’s Equations
EM Spectrum
Chapter 9
Ray Optics and Optical Instruments
Applications of TIR
Optical fibre cables
Mirage and Looming
Circle of illumination
TIR in prism
Microscope
Used to achieve linear magnification of very small objects (uses convex lens)
Simple Microscope
Uses a convex lens of small focal length
Compound Microscope
2 convex lenses:
Objective lens: Real, inverted, enlarged image, small focal length
Eye piece: Virtual, erect, enlarged image, large focal length
Telescope
A device that provides angular magnification to see distant objects
Has 2 convex lenses:
Objective Lens: Real, inverted, enlarged image, larger focal length and aperture
Eye piece: Virtual, erect, enlarged image, smaller focal length and aperture
Two types:
Astronomical
Terrestrial
Drawbacks of Refracting Telescopes
The lens can only be supported at the edges
Lenses have chromatic aberration
Advantages and Disadvantages of Reflecting Telescopes
Advantages:
The lens can be supported at the back
Don’t have chromatic aberration
Disadvantages:
Some rays of the object will be blocked by the observer
Chapter 10
Wave Optics
Huygen’s Principle
Each point of the wavefront is the source of a secondary disturbance and acts as a source of secondary disturbances called wavelets. These secondary wavelets propagate with speed of wave and their common tangent at a later time gives the new wavefront
Coherent Sources and Conditions
Two sources are said to be coherent if they have same phase or constant phase difference
The light waves emitted by the sources must have the same frequency and wavelength
Two independent sources of light can never be coherent
Incoherent Sources
Incoherent sources emit light waves having a different frequency, wavelength and phase
Diffraction of Light
The phenomenon in which light bends around the sharp edges of obstacles
Diffraction is only evident if the wavelength and the size of obstacle is almost same
Chapter 11
Dual Nature of Radiation of Matter
Work Function
The minimum energy required to remove an electron from the surface of a metal
Chapter 12
Atoms
Impact Parameter
It is the perpendicular distance of the initial velocity vector of α-particles from the centre of the nucleus
Distance of Closest Approach
The smallest distance an α-particle can go near the nucleus
Rutherford’s Model
+ve charged nucleus at the centre of the atom and electrons revolved around the nucleus in circular orbits
The centripetal force required for a dynamically stable orbit is given by the electrostatic force
Drawbacks of Rutherford’s Model
Could not explain stability of an atom: As electron revolves around the nucleus, it should emit radiation, lose energy and spiral into the nucleus
Could not explain line spectra: Emission of line spectra by gases could not be explained since this model predicts continuous spectra but cannot explain why
Bohr’s Postulates
Electrons could only revolve around the nucleus in stable orbits in which no radiation is emitted
An electron can revolve in orbits around the nucleus in which the angular momentum of electron is the integral multiple of h/2π
Drawbacks of Bohr’s Model
Could not explain the relative intensity of spectral lines
It is only applicable for H-like atoms
de-Broglie’s explanation on Bohr’s Model (second postulate)
According to de-Broglie electrons can exist in orbitals where the circumference of the orbit is the integral multiple of de-Broglie’s wavelength of electron
Chapter 13
Nuclei
Binding Energy of Nucleus
The energy required to bind the protons and neutrons inside the nucleus against the coulombic repulsion
For 30 < A < 170: Ebn is kiw
For A < 10: Nuclear fusion is energetically possible
For A > 230: Nuclear fission is energetically possible
Properties of Nuclear Force
Strongest of all fundamental forces; short range force
Has a saturation property; K.E per nucleon is almost a constant (8 MeV)
Charge independent; same for p-p, n-n, p-n
Nuclear Fission
The process in which a heavy nucleus breaks into smaller fragments with the release of energy
Eg: When uranium is bombarded by a neutron
Nuclear Fusion
The process in which two or more lighter nuclei join together to form a nucleus with the release of energy
Required very high temperatures (108 K) to overcome the coulombic repulsion and fuses. So it is called a thermonuclear reaction
Chapter 14
Semiconductor Electronics: Materials, Devices, and Simple Circuits
Semiconductors
Materials whose conductivity ranges between 105 - 10-6 S/m
Classified into elemental (pure Si or Ge) and compoundal (inorganic: PbS, GaAs; organic: anthracine)
Energy Bands and Energy Band Diagrams
Collection of closely spaced energy levels
Intrinsic semiconductors
Pure/undoped (Si or Ge)
In intrinsic semiconductors, the number of excited electrons is equal to the number of holes
It shows a low electrical conductivity under room temperature (insulator at 0K) and its conductivity depends on its temperature
Extrinsic semiconductors
Obtained when an impurity is added to intrinsic semiconductors
Adding impurities or dopants increases conductivity and this process is called doping
p-type Semiconductors
When an intrinsic conductor is doped with trivalent impurities (Al, In, B)
Majority carriers: holes
Minority carriers: electrons
In a p-type semiconductor, the hole density is much greater than the electron density
The acceptor energy level of the p-type is close to the valency bond and away from the conduction band
n-type Semiconductors
Obtained when an intrinsic conductor is doped with pentavalent impurities (P, As, Sb)
Majority carriers: electrons
Minority carriers: holes
In the n-type of semiconductor, the electron density is much greater than the hole density
The donor energy level of n-type is close to the conduction band and away from the valency band
p-n Junction diode
A junction known as the p-n junction is an interface or a boundary that is present between p and n-type semiconductor
The side which is known as the p-side or the positive side of the semiconductor has an excess of holes and the n-side or the negative side has an excess of electrons
Cannot be formed by joining separate p and n-type materials
A single waver of p-type material is doped with n-type material on one side and it forms a junction in the middle
When the junction forms, two processes occur:
Diffusion: Due to the difference in concentration of charge carriers; free electron diffusion from n-side to p-side; hole diffusion from p-side to n-side
Drift: During diffusion, a depletion region is created due to the recombining of electron-hole paris consisting of immobile donors and acceptors (no charge carriers). An electric field is established in the region due to immobile ions and it is directed from the n-side to the p-side
There is a potential barrier across PN junction that prevents charge carriers from crossing the junction at equilibrium (Idiffusion = Idrift; I = 0)
p-n Junction in forward bias
When the p-side is connected to the +ve terminal and the n-side is connected to the -ve terminal
The width of the depletion region reduces
Effective barrier height reduces and when the external voltage is equal to the barrier potential, the barrier disappears and charge carriers start crossing the junction resulting in a current flow
The diffusion current will be greater than the drift current
After cut-in voltage, the current increases rapidly and the diode offers less resistance
p-n Junction in reverse bias
When the p-side is connected to the -ve terminal and the n-side is connected to the +ve terminal
The width of the depletion region increases
Potential barrier increases
The motion of carriers from one side of the junction to another decreases
The drift current will be greater than the diffusion current
After the breakdown voltage, the current increases heavily
Ideal Diode
Vcut-in = 0
Vr = ∞
Rectifier
A device that converts AC to DC:
Half Wave Rectifier: step-down transformer; one diode
Full Wave Rectifier: centre-tap transformer; 2 diodes
Note 
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