FYUG Even Semester Exam, 2025

PHYSICS (4th Semester) | Course No.: PHYDSM-252 Subject: Electricity, Magnetism and Electronics Full Marks: 70 | Pass Marks: 28 | Time: 3 Hours

Instructions: The figures in the margin indicate full marks for the questions. Solve all questions including internal choices.

UNIT-I

[2 × 2 = 4]

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 / ε₀
This 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 + 8 = 10]

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

[6 + 2 + 2 = 10]

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:

Divergence: ∇ · B = 0 because magnetic monopoles do not exist; magnetic field lines always form closed loops.
Magnetic Vector Potential (A): A vector field whose curl is equal to the magnetic induction B, defined as
B = ∇ × A

UNIT-III

[4 + 2 + 4 = 10]

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):

  1. ∇ · D = ρ
  2. ∇ · B = 0
  3. ∇ × E = -∂B/∂t
  4. ∇ × H = J + ∂D/∂t
Displacement Current: It is the current that arises from a time-varying electric field, given by I_d = ε₀(∂Φ_E/∂t).
Equation of Continuity: Derived from the conservation of charge:
∇ · J + ∂ρ/∂t = 0

UNIT-IV

[6 + 4 = 10]

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

[6 + 2 + 2 = 10]

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

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