ELECTROMAGNETIC FIELDS
UNIT I  STATIC ELECTRIC FIELDS
PARTA (2 Marks)
1. Describe what are the source of electric field and magnetic fields?
2. What is a scalar quantity?
3. What is a vector quantity?
4. Define vector product of two vectors.
5. Find the dot product of the vectors A and B if A =2ax3ay+4az, B= ax+2ay+2az.
6. Write down expression for x,y,z in terms of spherical coordinates r,θ and Ф.
7. Represent point P (0, 1, 1) m given in Cartesian coordinates in spherical coordinates.
8. Give any three co ordinate systems.
9. Express the value of differential volume in rectangular and cylindrical coordinate systems.
10. Write expression for differential length in cylindrical and spherical co ordinates.
11. What is physical significance of divergence of D?
12. Express the divergence of a vector in the three system of orthogonal Coordination.
13. State divergence theorem.
14. State Stoke’s theorem.
15. How is the unit vectors defined in three co ordinate systems?
PARTB (16 Marks)
1. The electric field in a spherical coordinate is given by E = rρr / 5ε. Show that closed
∫E.dS=∫(▼.E)Dv. (16)
2. a. State and prove divergence theorem. (8)
b. What are the major source of electromagnetic fields (8)
3.Check validity of the divergence theorem considering the field D=2xy ax+x2
ay c/m2
and the
rectangular parallelepiped formed by the planes x=0,x=1,y=0,y=2 &z=0,z=3. (16)
4 .A vector field D = [5r2
/4]Ir is given in spherical coordinates. Evaluate both sides of divergence
theorem for the volume enclosed between r=1&r=2. (16)
5. Given A= 2r cosΦ+Riφ in cylindrical coordinates .for the contour x=0 to 1, y= 0 to1, verify
Stoke’s theorem (16)
6. Explain three coordinate systems. (16)
7. a. A uniform line charge ρL =25Nc/m lies on the x=3m and y=4m in free space.
Find the electric field intensity at a point (2, 3and 15) m. (8)
b. Given that potential V=10sinθcosΦ/r2 find the electric flux density D at (2, π/2,0) (8)
8. State and prove Gauss law and explain applications of Gauss law. (16)
9. Derive an expression for the electric field due to a straight and infinite uniformly charged wire of
length ‘L’ meters and with a charge density of +λ c/m at a Point P which lies along the perpendicular
bisector of wire. (16)
10. A circular disc of radius ‘a’ m is charged uniformly with a charge density of σ c/ m2
.find the
electric field at a point ‘h’ m from the disc along its axis. (16)
11. Define the potential difference and absolute potential. Give the relation between potential and
field intensity. (16)
12. Derive an expression for potential due to infinite uniformly charged line and also derive potential
due to electric dipole. (16)
UNIT II STATIC MAGNETIC FIELD
PARTA (2 Marks)
1. Define Lorentz law of force.
2. State BiotSavart Law.
3. State Ampere’s circuital law.
4. What is the difference between scalar and vector magnetic potential.
5. Define Magnetic Moment.
6. What is magnetic dipole moment?
7. Can a magnetic field exist in a good conductor if it is static or time varying? Explain.
8. Define magnetic vector potential.
PART B (16 Marks)
1. Derive the expression for magnetic field intensity and magnetic flux density due to finite and
infinite line. (16)
2. Derive the expressions for magnetic field intensity and magnetic flux density due to circular coil.
(16)
3. a. Derive an expression for force between two current carrying conductors (8)
b. An iron ring with a cross sectional area of 3cm square and mean circumference of
15 cm is wound with 250 turns wire carrying a current of 0.3A. The relative permeability
of ring is 1500.Calculate the flux established in the ring. (8)
4. a. Derive the expression for torque developed in a rectangular closed circuit carrying current I in a
uniform field. (8)
b. State Ampere’s circuital law and explain any two applications of Ampere’s Circuital law. (8)
UNIT III ELECTRIC AND MAGNETIC FIELDS IN MATERIALS
PARTA (2 Marks)
1. Write the Poisson’s and Laplace equations.
2. Obtain Poisson’s equation from Gauss’s law
3. What is displacement current?
4. What is a capacitor?
5. Define Magnetic dipole.
6. What is magnetic dipole moment?
7. Define magnetization.
8. Define magnetic susceptibility.
9. What is the relation between relative permeability and susceptibility?
10. What are the different types of magnetic materials?
11. Define magnetic flux?
12. Define mmf?
13. Define Reluctance and permeance?
14. State the boundary conditions at the interface between two perfect dielectrics.
15. Write down the magnetic boundary conditions.
16. Write the point form of Ohm’s law.
17. Define self inductance.
18. Define Mutual inductance.
PARTB (16 Marks)
1. Derive the boundary conditions of the normal and tangential components of electric field at the
interface of two media with different dielectrics. (16)
2. a. Derive an expression for the capacitance of a parallel plate capacitor having two dielectric
media. (8)
b. Obtain the expression for the energy stored in magnetic field (8)
3. Drive an expression for energy stored and energy density in an Electrostatic field (16)
4. a. Derive an expression for the capacitance of two wire transmission line. (8)
b. Derive an expression for capacitance of coaxial cable. (8)
5 Derive the boundary conditions of the normal and tangential components of magnetic field at the
inter face of two media with different dielectrics. (16)
6. a. Derive the expression for coefficient of coupling. (8)
b. Prove Laplace’s and Poisson’s equations. (8)
UNIT IV
TIME VARYING ELECTRIC AND MAGNETIC FIELDS
1. State Faraday’s law of induction.
2. State lenz’s law
3. Give the equation of transformer emf
4. What is motional electric field?
5. What is motional emf?
6. What is the emf produced by moving loop in time varying field?
7. What is time harmonic field?
8. Give time harmonic Maxwell’s equation in point form. Assume time factor eiωt
.
9. Distinguish between Field theory and Circuit theory
10. Write Maxwell’s equation in point and integral form for good conductors.
11. What is significance of displacement current density?
12. In a material for which σ= 5s/m and εr= 1 and E=250 sin 1010t (V/m).find the conduction and
displacement current densities.
13. Define Poynting vector.
14. State Poynting Theorem.
PARTB (16 Marks)
1. With necessary explanation, derive the Maxwell’s equation in differential and integral forms (16)
2. a. Write short notes on faradays law of electromagnetic induction. (8)
b. The magnetic field intensity in free space is given as H=H0sinθ ay t A/m. Where θ=ωtβz and β is
a constant quantity. Determine the displacement current density. (8)
3. a. What is the physical significance of the poynting vector? (4)
b. State and explain the pointing theorem. (12)
UNIT V
ELECTROMAGNETIC WAVES
1. Define a Wave.
2. Mention the properties of uniform plane wave.
3. Write down the wave equation for E and H in free space.
4. Write down the wave equation for E and H in a conducting medium.
5. Define intrinsic impedance or characteristic impedance.
6. Calculate the characteristic impedance of free space.
7. Define propagation constant.
8. Define skin depth δ
9. What is lossy dielectric medium?
10. For a loss dielectric material having µr=1, ε r=48, σ=20s/m. calculate the propagation constant at a
frequency of 16 GHz
11. Define Polarization.
12. Define Circular Polarization.
13. Define Elliptical polarization.
14. Define Linear Polarization.
PARTB (16 Marks)
1. A plane wave propagating through a medium with εr=8, µr=2 has E=0.5 sin (108
tβz) az v/m.
Determine
(i) β
(ii) The loss tangent
(iii) wane impedance
(iv) wave velocity
(v) magnetic field (16)
2. Derive a wave equation for non dissipative medium making use of Maxwell equations and field
vectors E and H. (16)
3. A plane sinusoidal electromagnetic wave traveling in space has Emax=150µV/m.
(i)Find the accompanying Hmax
(ii)Propagation is in X direction and H is oriented in Y direction. What
is the direction of E.
(iii) Compute the average power transmitted. (16)
4. Define wave. Derive the free space electromagnetic wave equation. (16)
5. Discuss about the plane waves in lossy dielectrics. (16)
6. Discuss about the plane waves in lossless dielectrics. (16)
7. Briefly explain about the wave incident
(i) Normally on perfect conductor
(ii) Obliquely to the surface of perfect conductor. (16)
