UNIT –I: INTRODUCTION
Part A
1. State divergence theorem.
2. State Stoke’s theorem.
3. What is del operator? How is it used in density curl, gradient and divergence?
A = x ax + y ay+ y az
4. Define vector product of two vectors.
5. Write down expression for x, y, z in terms of spherical co-ordinates r,θ and φ.
6. Write down the expression for differential volume element in terms of spherical
co-ordinates.
7. What is the divergence of curl of a vector?
8. Write expression for differential length in cylindrical and spherical co-ordinates.
9. Find the divergence of F= x y ax+ y x ay + z x az
10. Define a vector and its value in Cartesian co-ordinate axis.
11. Verify that the vectors A= 4 ax - 2ay + 2az and B = -6ax + 3ay - 3az are parallel to each other.
12. List out the sources of electromagnetic fields.
13. When a vector field is solenoidal and irrotational.?
Part B
14. (i) State and prove Divergence theorem.
(ii) For a vector field A, show explicitly that ∆.∆ x A=0: that is the divergence of the curl of any vector field is zero.
15. (i) State and prove Stroke’s theorem.
(ii) Show that the vector H = (y2- z2+3yz-2x) ax + (3xz+2xy) ay + (3xy- 2xz+2z) az is both irrotational and solenoidal.
16. Using Divergence theorem, evaluate ∫∫ E.ds = 4xz ax - y2 ay + yz az over the cube bounded by x=0,x=1,y=0,y=1,z=0,z=1
17. What is the different co-ordinate systems used to represent field vectors? Discuss about them in brief.
18. (i) Given A= 5 ax and B= 4 ax + t ax Find t such that the angle between A and B is 45.
(ii) Using Divergence theorem evaluate ∫∫ A.ds where A = 2xy ax + y2 ay + 4yz az and S is the surface of the cube bounded by x =0 , x = 1; y = 0, y = 1; and z = 0, z = 1.
19. (i) Determine the divergence and curl of the vector A = x ax + y ay+ y az
(ii) Determine the gradient of the scalar field at P(√2, л/2, 5) defined in cylindrical co-ordination system as A = 25 r sin Ф.
20. Given point P(-2,6,3) and vector A= y ax + (x+z) ay Evaluate A and at P in the Cartesian, cylindrical and spherical systems
UNIT II: ELECTROSTATICS
Part A
1. State coulomb’s law.
2. State Gauss’s law.
3. Define dipole moment.
4. Define electric flux and flux density.
5. Define electric field intensity or electric field.
6. What is a point charge?
7. Write the Poisson’s and Laplace equation.
8. Define potential and potential difference.
9. Give the relationship between potential gradient and electric field.
10. Define current density.
11. State point form of Ohm’s law.
12. Define polarization.
13. Express the value of capacitance for a coaxial cable.
14. What is meant by displacement current?
15. State the boundary conditions at the interface between two perfect dielectrics.
16. Write down the expression for the capacitance between (a) two parallel plates (b) two coaxial cylinders.
17. Calculate the capacitance of a parallel plate capacitor having an electrode area of 100 cm2. The distance between the electrodes is 3 mm and the dielectric used has a permittivity of 3.6 the applied potential is 80 V. Also compute the charge on the plates.
18. An infinite line charge charged uniformly with a line charge density of 20 n C/m is located along z-axis. Find E at (6, 8, 3) m.
Part B
19. (i) Derive an expression for electric field due to an infinite long charge from its principles.
(ii)Derive the boundary conditions at the charge interfaced of two dielectric media.
20. Find the electric field intensity due to the presence of co-axial cable with inner conductors of ρs c/m2 and outer conductor of - ρs c/m2.
21. What is dipole? Derive the expression for potential and electric field intensity due to a dipole.
22. (i) Compare and explain conduction current and displacement current.
(ii) A circular of radius ‘a’ meter is charged uniformly with a charge density ρs c/m2. Find the electric field at a point ‘h’ meter from the disc along its axis.
23. A circular disc of 10cm radius is charged uniformly with a total charge of 10^-6 C. Find the electric intensity at a point 30cm away from the disc along the axis.
24. (i) Derive the expression for electric field intensity due to a circular surface charge.
(ii) Two parallel plates with uniform surface charge intensity equal and opposite to each other have an area of 2 m2 and distance of separation of 2.5 mm in free space. A steady potential of 200 V is applied across the capacitor formed. If a dielectric of width 1 mm is inserted into this arrangement what is the new capacitance if the dielectric is a perfect non- conductor?
25. (i) State and prove Gauss’s law.
(ii) Derive an expression for energy density in electrostatic fields.
26. (i) Derive Poisson’s and Laplace equation.
(ii) Three concentrated charges of 0.25 µ C are located at the vertices of an equilateral triangle of 10 cm side. Find the magnitude and direction of the force on one charge due to other two charges.
27. (i) Using Laplace’s equation find the potential V between two concentric circular cylinders, if the potential on the inner cylinder of radius 0.1 cm is 0Vand that on the outer cylinder of radius 1 cm is 100 V.
(ii) A point charge of 5 n C is located at (-3, 4,0 ) while line y = 1, z = 1 carries uniform charge 2 n C/m. If V =0V at O (0, 0, 0) find V at A (5, 0, 1)
UNIT III
MAGNETOSTATICS
Part A
1. State Ampere’s circuital law.
2. State Biot-Savart law.
3. State Lorenz law of force.
4. Define magnetic scalar potential.
5. Write down the equation for general, Integral and point form of Ampere’s law.
6. What is field due to toroid and solenoid?
7. Define magnetic flux density.
8. Write down the magnetic boundary conditions.
9. Give the force on a current element.
10. Define magnetic moment.
11. Give torque on a solenoid.
12. State Gauss’s law for magnetic field.
13. Define magnetic dipole.
14. Define magnetization.
15. Define magnetic susceptibility.
16. What are the different types of magnetic materials?
17. What is the inductance per unit length of a long solenoid of N turns and having a length L meters?Assume that its carries a current of I amps.
18. A parallel plate capacitor with plate area of 5 cm2 plate separation of 3 mm has a voltage 50 sin 103 t applied to its plates. Calculate the displacement current assuming ξ= 2 ξ0
Part B
19. (i) Derive an expression for the force between two current carrying wires.Assume that the currents are in the same direction.
(ii) State and explain Biot-Savart’s law.
20. Obtain an expression for the magnetic field around long straight wire using magnetic vector potential.
21. (i) Obtain an expression for the magnetic flux density and field intensity due to finite long current carrying conductor.
(ii) Give a brief note on the magnetic materials.
22. Derive the expression for magnetic field intensity on the axis of solenoid at a) center and b) end point of the solenoid.
23. (i) State and explain Ampere’s circuital law.
(ii) State and prove boundary condition for magnetic field.
24. Derive an expression for the inductance of solenoid and toroid.
25. Derive an expression for the inductance per meter length of two transmission lines.
26. Obtain the expression for energy stored in magnetic field and also derive an expression for magnetic energy density.
27. (i) Derive and expression for self inductance of co-axial cable.of inner radius a and outer radius radius b.
(ii) A circular loop located on x2+y2 =9, z=0 carries a direct current of 10 A along aθ. Determine H at (0,0, 4) and (0,0,-4).
28. An air coaxial transmission line has a solid inner conductor of radius ‘a’ and very thin outer conductor of inner radius ‘b’. Determine the inductance per unit length of the line.
UNIT IV
ELECTRODYNAMIC FIELDS
Part A
1. State Faraday’s law of electromagnetic induction.
2. Define self inductance.
3. Define mutual inductance.
4. Define coupling coefficient.
5. Define reluctance.
6. Give the expression for lifting force of an electromagnet.
7. Give the expression for inductance of a solenoid.
8. Give the expression for inductance of a toroid.
9. What is energy density in the magnetic field?
10. Define permeance.
11. Distinguish between solenoid and toroid.
12. Write down the general, integral and point form of Faraday’s law.
13. Distinguish between transformer emf and motional emf.
14. Compare the energy stored in inductor and capacitor.
15. State Lenz’s law.
16. Define magnetic flux.
17. Write the Maxwell’s equations from Ampere’s law both in integral and point forms.
18. Write the Maxwell’s equations from Faraday’s law both in integral and point forms.
19. Write the Maxwell’s equations for free space in point form.
20. Write the Maxwell’s equations for free space in integral form.
21. Determine the force per unit length between two long parallel wires separated by 5 cm in air and carrying currents of 40 A in the same direction.
Part B
22. (i) State and explain Faraday’s law.
(ii)Compare the field theory and circuit theory.
23. Develop an expression for induced emf of Faraday’s disc generator.
24. Derive the Maxwell’s equation for free space in integral and point forms explain.
25. Derive Maxwell’s equation from Faraday’s law and Gauss’s law and explain them.
26. Derive the Maxwell’s equation in phasor differential form.
27. Derive the Maxwell’s equation in phasor integral form.
28. Derive and explain the Maxwell’s equations in point form and integral form using Ampere’s circuital law and Faraday’s law.
ELECTROMAGNETIC WAVES
Part A
1. Define a wave.
2. Mention the properties of uniform plane wave.
3. Define intrinsic impedance or characteristic impedance.
4. Calculate the characteristics impedance of free space.
5. Define propagation constant.
6. Define skin depth.
7. Define polarization.
8. Define linear polarization.
9. Define Elliptical polarization.
10. Define pointing vector.
11. What is complex pointing vector?
12. State Slepian vector.
13. State pointing theorem.
14. State Snell’s law.
15. What is Brewster angle?
16. Define surface impedance.
17. Write the wave equation in a conducting medium.
18. Compute the reflection and transmission coefficients of an electric field wave travelling in air and incident normally on a boundary between air and a dielectric having permittivity of 4.
19. Calculate the depth of penetration in copper at 10 MHZ given the conductivity of copper is 5.8 x 10 7 S/m and its permeability = 1.3=26 mH/m.
Part B
1. (i) Obtain the electromagnetic wave equation for free space in terms of electric field.
(ii)Derive an expression for pointing vector.
2. (i) Obtain the electromagnetic wave equation for free space in terms of magnetic field.
(ii) Calculate the intrinsic impedance, the propagation constant and wave velocity for a conducting medium in which σ = 58 ms/m, µ r = 1 at a frequency of f = 100 M Hz.
3. (i) Derive the expression for characteristic impedance from first principle.
(ii)Show that the intrinsic impedance for free space is 120π. Derive the necessary equation.
4. (i) Explain the wave propagation in good dielectric with necessary equation.
(ii)Define depth of penetration. Derive its expression.
5. (i) Derive the expressions for input impedance and standing wave ratio of transmission line.
(ii) Find the skin depth at a frequency of 1.6 MHz in aluminium σ= 38.2 ms/m and µr = 1.
6. (i) State and prove pointing theorem.
(ii) Define surface impedance and derive its expression.
7. Define Brewster angle and derive its expression. Also define loss tangent of a medium.
8. Determine the reflection coefficient of oblique incidence in perfect dielectric for parallel polarization.
