Field theory- model question paper for MSc Physics/ B.E/B.Tech Electronics

1(a) transform the vector A = ya_x – xa_y + za_z into cylindrical coordinates. (04 marks)

(b) Determine the electric field intensity on the axis of a circular conductor (ring) of linear charge density ρ_L.(06 Marks)

(c) Determine using gauss’s law, the electric field due to a sphere of charge of radius, a. The charges are uniformly distributed over a spherical surface with a distribution ρ_s. (06 Marks)

(d) An infinitely long line charge of uniform density, ρ_L produces an electric field. Show that the divergence of this electric field is zero everywhere except at the line. (04 marks)

2(a) Write a note on equipotential surface. (04 Marks)

(b) Three identical line charges with ρ_L= 10 nC/m are placed on each of the coordinate axes of a rectangular coordinate system. Given the points A(1,2,3) and B(8,6,10), find V_AB due to all the three line charges. (06 Marks)

(c) Show that the gradient of the scalar field, V (x,y) = x-y (V) is normal to the planes of constant V. (05 Marks)

(d) What is an electric dipole? Mention one application. (05 marks)

3(a) Ina cylindrical electron beam of radius R and unit length, the volume charge density is given by, ρ_v = Kρ, where K is some arbitrary constant. Determine the energy stored in the beam. (08 Marks)

(b) Distinguish between convection current and conduction current. (06 Marks)

(c) A copper wire of cross sectional area, 10 ^-4 m² carries a uniformly distributed current of 200 A. If the electron density in copper is 4.25×10²⁸ electrons/m³, determine the average drift velocity of the electrons. What is the electric field in the wire? If the length of the wire is 10⁵ m, calculate the potential difference between its ends. What is the resistance of the wire? (06 Marks)

4 (a) Write a note on boundary conditions for perfect dielectric materials. (06 Marks)

(b)  Determine the capacitance of a parallel plate capacitor consisting of two parallel conducting plates of area A and separation d. (06 Marks)

(c) Find the capacitance of an isolated conducting sphere of radius a. (04 Marks)

(d) What is Poisson’s equation? Explain. (04 Marks)

5 (a) State and explain Uniqueness theorem. (06 Marks)

(b) In a charge free region of free space, the potential field is given as V (x,y) = x³-f(x)-y². Find f(x) if E and V are zero at (0,0,0). (06 marks)

(c) Determine magnetic field due to a current, I flowing in a straight conductor of length 2L. (08 Marks)

6(a) Explain Ampere’s circuital law. (04 Marks)

(b) Write down Maxwell’s equations. (04 Marks)

(c) Show that the magnetic flux density B set up by an infinitely long current carrying conductor satisfies the Gauss’s law. (06 Marks)

(d) Write a note on scalar and vector magnetic potentials. (06 Marks)

7 (a) Explain the terms magnetic susceptibility and relative permeability. (04 marks)

(b) Find the self inductance per unit length of an infinitely long solenoid. (04 Marks)

(c) A steady current is restricted to flow on the outer surface of the inner conductor (ρ = a) and the inner surface of the outer conductor (ρ = b) in a coaxial cable. If the coaxial cable carries a current, I, determine the energy stored per unit length in the magnetic field in the region between the two conductors. Assume that the dielectric is non-magnetic. (06 Marks)

(d) Consider two coupled circuits having self-inductances L₁ and L₂ that carry currents I₁ and I₂ respectively. The mutual inductance between the two coupled circuits is M₁₂. Determine the ratio I₁/I₂ that makes the stored magnetic energy, W_m a minimum. (06 Marks)

8 (a) From Faraday’s law, derive Maxwell’s equation in point form. (04 marks)

(b) The dry earth has a conductivity 10^-8 S/m and a relative permeability 4. Find the frequency range on which the conduction current dominates the displacement current. (04 Marks)

(c) Write the phasor and time-domain forms of a uniform plane wave having a frequaency of 1 (GHz), that is traveling in the +x direction in a medium of ε = 12ε₀ and µ = µ₀ (06 Marks)

(d) What are Snell’s laws? Explain. (06 Marks)