FYUG Even Semester Exam, 2025
Instructions: The figures in the margin indicate full marks for the questions. Solve all questions including internal choices.
UNIT-I
1. Answer any two questions
(a) State and explain Gauss's law of electrostatics.
Answer: Gauss's law states that the total electric flux through any closed surface is equal to 1/ε₀ times the net charge enclosed by that surface.
Mathematically:Φ = ∮ E · dA = q_enclosed / ε₀This law relates the distribution of electric charge to the resulting electric field.
(b) Define electric field and electric flux.
Answer:
- Electric Field: It is defined as the force experienced per unit positive test charge placed at a point in space.
- Electric Flux: It is the measure of the total number of electric lines of force passing normally through a given area.
(c) Write down the properties of electric lines of force.
Answer:
- They start from a positive charge and end on a negative charge.
- They never intersect each other.
- The tangent to a line of force at any point gives the direction of the electric field at that point.
- They are continuous curves without any sudden breaks.
2. (a) Electric Field of Spherical Shell
Define electric charge (SI unit) and derive the expression of electric field due to a uniformly charged spherical shell at points inside and outside.
Answer: Electric Charge: It is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. The SI unit is the **Coulomb (C)**.
Derivation: Consider a spherical shell of radius R with charge Q. 1. Outside the shell (r > R): Construct a Gaussian sphere of radius r. By Gauss's Law: E(4πr²) = Q/ε₀ ⇒
E = Q / (4πε₀r²)2. Inside the shell (r < R): Since the charge resides on the surface, q_enclosed = 0. By Gauss's Law: E(4πr²) = 0 ⇒
E = 0
UNIT-II
4. (a) Magnetic Materials
Define diamagnetic, paramagnetic, and ferromagnetic materials with examples. Why is the divergence of magnetic field zero? What is magnetic vector potential?
Answer:
- Diamagnetic: Feebly repelled by magnets (e.g., Bismuth).
- Paramagnetic: Feebly attracted by magnets (e.g., Aluminum).
- Ferromagnetic: Strongly attracted by magnets (e.g., Iron).
Magnetic Vector Potential (A): A vector field whose curl is equal to the magnetic induction B, defined as
B = ∇ × A
UNIT-III
6. (b) Maxwell's Equations
Write down Maxwell's equations, define displacement current, and obtain the equation of continuity.
Answer: Maxwell's Equations (Differential Form):
- ∇ · D = ρ
- ∇ · B = 0
- ∇ × E = -∂B/∂t
- ∇ × H = J + ∂D/∂t
Equation of Continuity: Derived from the conservation of charge:
∇ · J + ∂ρ/∂t = 0
UNIT-IV
8. (a) Rectifier and Zener Diode
Explain the working of a full-wave rectifier and how a Zener diode acts as a voltage regulator.
Answer: Full-Wave Rectifier: Uses two diodes (center-tap) or four (bridge) to convert both halves of the AC cycle into DC. During the positive half, D1 conducts; during the negative half, D2 conducts, ensuring current flows in the same direction through the load.
Zener Voltage Regulator: Operated in the reverse breakdown region.
When the input voltage increases, the Zener current increases, but the voltage across the Zener (and thus the load) remains constant at V_z.UNIT-V
10. (a) Universal Gates
Explain NAND and NOR gates, why they are universal, and define XOR gate.
Answer:
NAND & NOR: NAND is an AND followed by NOT; NOR is an OR followed by NOT.
Universal Property: They are called universal because any basic logic gate (AND, OR, NOT) can be realized using only NAND or only NOR gates.
XOR Gate: Exclusive OR gate; output is HIGH only when the inputs are different.
Y = A⊕B = AB' + A'B