Paper 3

Core 3: Electricity and Magnetism

Syllabus

(Basic concepts and various phenomena in Electricity and Magnetism, Circuit analysis and network theorems, Dynamics of Charged Particles.)

Unit 1 Electric Field and Electric Potential

• Electric field: Electric field lines, Electric flux, Gauss Law with applications to charge distributions with spherical, cylindrical and planar symmetry, Conservative nature of Electrostatic Field. Electrostatic Potential, Potential and Electric Field of a dipole, Force and Torque on a dipole, Potential calculation in different simple cases, Laplace and Poisson equations, The Uniqueness Theorem, Method of Images and its application to (1) Plane Infinite Sheet and (2) Sphere.
• Electrostatic energy of system of charges, Electrostatic energy of a charged sphere, Conductors in an electrostatic Field, Surface charge and force on a conductor.

Unit II Magnetic Field

• Magnetic Force, Lorentz Force, Biot Savarts Law, Current Loop as a Magnetic Dipole and its Dipole Moment (analogy with Electric Dipole), Amperes Circuital Law and its application to (1) Solenoid (2) Toroid (3) Helmhotz coil, Properties of curl and divergence, Vector Potential, Ballistic Galvanometer: Torque on a current Loop, Current and Charge Sensitivity, Electromagnetic damping, Logarithmic damping, CDR.

Unit III

Dielectric Properties of Matter: Electric Field in matter, Polarization, Polarization Charges, Electrical Susceptibility and Dielectric Constant, Capacitor (parallel plate, spherical, cylindrical) filled with dielectric, Displacement vector D, Relations between E, P and D, Gauss Law in dielectrics. Magnetic Properties of Matter: Magnetization vector(M), Magnetic Intensity(H), Magnetic Susceptibility and permeability, Relation between B, H, M, Ferromagnetism, B-H curve and hysteresis. Electromagnetic Induction: Faradays Law, Lenz’s Law, Self-Inductance and Mutual Inductance, Reciprocity Theorem, Energy stored in a Magnetic Field, Introduction to Maxwell’s Equations.

Unit IV

• Electrical Circuits: AC Circuits: Kirchhoffs laws for AC circuits, Complex Reactance and Impedance,
• Series LCR Circuit: (1) Resonance (2) Power Dissipation (3) Quality Factor, (4) Band Width, Parallel LCR Circuit.
• Network theorems: Kirchoff’s law for electrical circuits, Ideal Constant-voltage and Constant-current Sources.
• Network Theorems: Thevenin theorem, Norton theorem, Superposit io n theorem, Reciprocity theorem, Maximum Power Transfer theorem, Applications to DC circuits. Transient Currents Growth and decay of current in RC and LR circuits.

Text Books:

• Introduction to Electrodynamics – D. J. Griffiths (Pearson, 4th edition, 2015)
• Foundations of Electromagnetic Theory-Ritz and Milford (Pearson)

Reference Books:

• Classical Electrodynamics, J. D. Jackson (Wiley).
• Electricity and Magnetism D. C. Tayal (Himalaya Publishing house)
• Electricity, Magnetism and Electromagnetic Theory- S. Mahajan and Choudhury (Tata McGraw Hill)
• Feynman Lectures Vol. 2, R. P. Feynman, R. B. Leighton, M. Sands (Pearson)
• Electricity and Magnetism, J. H. Fewkes and J. Yarwood. Vol. I (Oxford Univ. Press)
• Classical Electromagnetism, H.C.Verma, Bharati Bhawan

---

Questions

2025 | +3-II-S-NEP-Major-I-P-3-Sc-Phy | Full Marks: 100

PART-I | Answer all the following Questions. | 1x10

1. The SI unit of electric flux is _____.
2. The unit of impedance is _____.
3. The electrostatic field is always a _____ field.
4. The SI unit of magnetic field is _____ .
5. The direction of force on a moving charge in a magnetic field is given by _____ .
6. The magnetic moment of a current loop is equal to ______ .
7. The relation between electric displacement vector, polarization and electric field is ______.
8. The magnetic susceptibility of a perfect diamagnet is _.
9. The hysteresis curve shows the relation between ______.
10. The maximum power transfer theorem states that maximum power is transferred when load resistance is equal to _____ .

PART-II | Answer the following question. | 2x9

1. Write Laplace and Poisson's equations.
2. A circular coil of radius 0.1 m has 50 turns and carries 2 A current. Find the magnetic moment.
3. State and explain the Lorentz Force Laws.
4. A coil of inductance 0.5 H carries a current of 2 A. Find the energy stored.
5. State Faraday's Law of electromagnetic induction.
6. A 20 V DC source is connected across a 10 Ω resistor. find the power dissipated.
7. In a series LCR circuit, L=0.1 H, C=100μF, R=10 Ω. Find resonant frequency.
8. State the maximum power transfer Theorem.
9. A parallel-plate capacitor with area 1 m², separation 0.01m, and dielectric constant 5 is connected to a 100 V source. Find the capacitance.

PART-III | Answer any eight questions of the followings. | 5x8

1. State and explain Gauss's law. Apply it to find the electric field due to a uniformly charged spherical shell.
2. Derive the expression for electrostatic potential and electric field due to an electric dipole.
3. What is the method of images? Apply it to find the potential distribution for an infinite grounded conducting plane.
4. State and explain Ampere's circuital law. Apply it to find the magnetic field inside a long solenoid.
5. Derive Biot-Savart law and explain its applications.
6. Define polarization. Derive an expression for electric field inside a dielectric.
7. Explain magnetic hysteresis and B-H curve with neat diagram.
8. Derive the expression for resonance in a series LCR circuit. Define quality factor and bandwidth.
9. State and explain Thevenin's theorem with an example.
10. Derive the expression for transient growth of current in an LR circuit.

PART-IV | Answer any four of the following. | 8x4

1. Derive Laplace's and Poisson's equations from Gauss's law and explain the uniqueness theorem.
2. Explain Helmholtz coil arrangement and derive the condition for producing a uniform magnetic field.
3. Explain magnetic hysteresis and B-H curve with neat diagram.
4. Define polarization. Derive an expression for electric field inside a dielectric.
5. State and derive Norton's theorem and explain its applications in DC circuits.