Vector Analysis

• Scalar and vectors

Scalar quantities
Vector quantities

• Some fundamental definitions in vector algebra
• Addition and subtraction of vectors
• Product of two vectors

Scalar product
Vector product

• Product of three vectors

Scalar triple product
Vector triple product

• Scalar and vector field
• Gradient of scalar field
• Divergence of a vector field
• Curl of a vector field
• Second derivatives of a vector field
• Line integral
• Surface integral and flux of vector field
• Volume integral
• Gauss’s divergence theorem
• Stokes’ theorem

Electrostatics in Vacuum

• Frictional electricity
• Charge and its properties

Types of charges
Quantization of charge
Conservation of charge
Basic properties of charge

• Coulomb’s law

Unit of charge
Coulomb’s law in vector form
Some important knowledge related to Coulomb’s law

• Force between many charges and superposition principle
• Continuous distribution of charges
• Electric field

Electric field intensity
Electric field due to a point charge
Electric field due to different charge distribution
Electric field due to a circular loop of charge
Electric field due to an infinitely long straight, uniformly charged wire

• Introduction of electrostatic potential or electric potential
• Electrostatic potential difference
• Electric potential at a point due to a point charge
• Relation between electric field and electric potential : Electric field as the gradient of potential
• Potential due to an arbitrary distribution of charge
• Electric potential energy
• Electric dipole
• Electric dipole moment
• Electric field due to dipole

Electric potential due to an electric dipole
Electric field due to dipole
Direction of electric field

• A dipole in an electric field

In uniform electric field
In non-uniform electric field

• Electric multipoles
• Electric quadrupole

Electric potential at P due to quadrupole
Electric field at P due to quadrupole
Potential due to multipole

• Multipole approximation to an arbitrary distribution of charge
• Equipotential surface and its properties
• Electric flux
• Gauss’s theorem or Gauss’s law in electrostatics
• Applications of Gauss’s law

Electric field due to a uniformly charged thin spherical shell or spherical conductor
Electric field due to a uniformly charged non-conducting sphere or spherical charge distribution
Electric field due to an infinite plane sheet of charge
Electric field due to an infinite charged conducting plate
Electric field due to an infinite long line charge

• Electrostatic energy of a uniformly charged sphere
• Classical radius of an electron)
• Force on the surface of a charged spherical conductor

Electric Field Around Conductor

• Introduction
• Poisson’s and Laplace equations

Laplacian operator in cartesian coordinate system
Laplacian operator in spherical polar coordinate system
Laplacian operator in cylindrical polar coordinate

• Boundary conditions
• Uniqueness theorem
• Solution of Laplace equation in cartesian coordinate system
• Potential at a point inside a rectangular body
• Electrical image method

Electric Field in Matter

• Coulomb’s law of force
• Atomic and molecular dipoles
• Polarization

Calculation of atomic polarizability (α)
Polarization density P
Permanent dipole moment
Electric polarization vector

• Capacitors

Parallel plate capacitor
Capacity of a parallel plate capacitor completely filled with dielectric
Capacity of a parallel plate capacitor partially filled with dielectric
Dielectric Strength

• The field of a charge in dielectric medium and Gauss’s law
• Electrostatic energy of a charge distribution in dielectric
• Lorentz local field and Clausius-Mossoti equation
• Dielectric sphere placed in a uniform field
• Field equations in electrostatics

Magnetostatics

• Oersted experiment magnetic field due to current

Ampere’s swimming rule
Right hand thumb rule
Maxwell’s cork screw rule
Magnetic field

• Magnetic flux density and magnetic flux
• Fleming’s left hand rule
• Biot-Savart law or Laplace’s law
• Applications of Biot-Savart law

Magnetic field due to a long and straight current carrying conductor
Magnetic field near a straight current filament or conducting wire of finite length
Magnetic field along the axis of current carrying circular coil

• Magnetic dipole and current loop
• Magnetic Lorentz force : Force on a moving charge in a magnetic field
• Unit of magnetic field
• Force on a current carrying conductor
• Ampere’s law

Ampere’s law in curl form or curl B

• Applications of Ampere’s law

Magnetic field due to a long current carrying wire
Magnetic field due to a long solenoid
Magnetic field due to a toroid

• Divergence of B
• Torque on a current carrying loop in magnetic field
• Magnetic field in matter
• Atom as a magnetic dipole

Expression for orbital magnetic moment
Expression for spin magnetic moment

• Some important definitions used in magnetism
• Relation between magnetic permeability and susceptibility
• Comparison of magnetostatics and electrostatics

Electric Current

• Introduction)
• Flow of charge in a conductor : Electric current
• Current density
• Equation of continuity

For steady fields
For time varying field

• Drift velocity and mobility
• Relation of electric current with drift velocity and mobility
• Electrical resistance, resistivity, conductance and conductivity

Electron theory of resistivity and conductivity
Classification of material on the basis of electrical conductivity
Effect of temperature on resistance
Superconductivity

• Non-ohmic circuitry
• Thermistors
• Thermoelectricity

Seebeck effect
Origin of thermo e.m.f.

• Growth and decay of current in LR-circuit
• Growth and decay of current in RC-circuit
• Differentiating circuits
• Integrating circuits
• Comparison of differentiating and integrating circuits
• Electrical shielding
• Study of a discrete transmission line

Alternating Current Circuit

• Alternating current
• Circuit analysis and representation of a.c. circuit quantities using complex number system
• Impedance of LCR series circuit and its quality factor
• Parallel or branched a.c. circuit and their resonance
• Comparative study of a series resonance and a parallel resonance circuit
• Power dissipation or power factor
• Principle of a.c. bridges
• Anderson’s bridge
• de-Sauty’s bridge
• Owen’s bridge
• Self inductance
• Mutual inductance
• Neumann’s formula
• Energy stored in magnetic field
• Coupled circuits
• Coefficient of coupling
• Transformer
• Skin effect for resistance at high frequencies

Moving Coil Ballistic Galvanometer and Its Applications

• Ballistic galvanometer
• Moving coil ballistic galvanometer

Current sensitivity, I_s
Charge sensitivity, Q_s

• Condition when a moving coil galvanometer is dead beat or ballistic
• Logarithmic decrement

Experimental determination of logarithmic decrement
Calibration of the ballistic galvanometer
Figure of merit of galvanometer

• Applications of B.G.

Measurement of mutual inductance by Carey Foster’s bridge method
Determination of the intensity of strong magnetic field using search coil
Measurement of low resistance by Kelvin’s double bridge
Measurement of high resistance by leakage method

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