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**Anna University Question Paper**

**B.E./B.Tech. DEGREE EXAMINATION, May /June 2014.**

**Electronics and Communication Engineering**

**2 nd year**

**4th Semester**

**EC2253-Electromagnetic Fields**

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Part A

1. In XY plane Q1=100100𝜇𝐶 at (2,3)m,experiences a repulsive force of 7.5N

because of Q2 at(10.6).Find Q2.

2. What is gradient.

3. If the magnetic field B=25𝑥𝑖 + 12𝑦𝑗 + 𝛼𝑧𝑘 (T),find α.

4. Write Biot Savart law.

5. An infinite solenoid (n turns per unit length current I)is filled with a linear material

of susceptibility Xm.Find the magnetic field inside the solenoid.

6. Write the boundry conditions for electric field.

7. Find the pointing vector on the surface of a long straight conducting wire (of

radius b and conductivity)that carries a dirct current I.

8. Stae the flux rule for a nonrectangular loop moving through a nonuniform

magnetic field.

9. A sinusoidal electric intensity of amplitude 250 N/M and frequency 1GHz exists

in lossey dielectric medium that has a relative permittivity of 2.5 and loss tangent

of 0.001.Find the effective conductivity of the lossy medium.

10. What is Skin depth.

Part B

11 a)1] State and Explain the fundamental theorem of divergence and curl.(8)

2]Find the electric field at distance ‘z’ above the center of a flat circular disc of radius

R,Which carries a uniform surface charge σ. (8)

Or

b) 1]Get the relationship between potential and electric field .A dipole consists of two

equal and opposite charges separated by distance d.Find the approximate potential at

points far from the dipole.(6)

2] Find the electric field at distance ‘z’ above the center of a circular loop of radius

r,which carries a uniform line of charge λ(5)

3]Given below the electric field variation find the odd one out (5)

1)E=c(xyi+2yzj+3xzk)

2)E=c(𝑦2𝑖 + 2𝑥𝑦 + 𝑧2𝑗 + 2𝑦𝑥𝑘

12 )a)1)Find the magnetic field at the centre of a square loop which carries a steady

current I,Let R be the distance from the centre to side.Find the field at the center of

a n-sided polygon,carrying a steady current I.Again let R be the center to any side

.Find the formula in the limit ntends to infinity.(8)

2)Find the magnetic field a distance h above the center of a circular loop of radius

R,which carries a steady current I.(8)

Or

b) 1) Derive the Ampere circuital law.(8)

2) Derive the expressions with mutually relate current density J,Magnetic field

B,Magnetic vector potential A.(8)

13) a)1]Derive the expression for the nergy of a point charge distribution .Three point

charges -1nC,4nC,3nC are located at (0,0,0),(0,0,1),(1,0,0) respectively.Find the energy

in the system.(8)

2]A small loop of wire (radis a)lies a distance z above the centre of a large loop (radius b)

The planes of the two loops are parallel and perpendicular to the common axis.Suppose

current I flows in the big loop Find the flux through the little loop.Find the mutual

inductance.(8)

Or

b).1]Write the poission’s and laplace equations(4)

2]Discuss the magnetic boundry conditions (6)

3]Two concentric metal spherical shells of radii a and b are separated by weakly

conducting material of conductivity σ If ther arwe maintained at a potential difference V

What current flows from one to another What is the resistance between the shells?Find

the resistance if b>>a(6)

14) a)1]Explain Ampere’s Circuit law. (8)

2]Derive poynting theorem .(8)

Or

b)1]Desribe the Maxwell’s equations in differential and integral forms.(8)

2]Write faraday’s law in differential and integral forms and explain faradays

experiments(8)

15)a)1]Derive the wave equations for electric and magnetic fields (8)

2].The electric field intensity of a linearly polarized uniform plane wave propagating in

the +z direction in sea water is E=100cos(107𝜋𝑡)𝑖 V/mat z=0.the constitutive parameters

of sea water are £r=72,μr=1,and conductivity σ=4 S/m. Determine the attenuation

constant,phase constant,intrinsic impedance,phase velocity,wavelength,skin depth.Also

find the distance at which the amplitude of E is 1% of its value at z=0. (8)

Or

b) 1]Analyse the wave behavior at boundaries under oblique incidence and derive the

Brewster angle.(12)

2]Prove that a linearly polarized wave can be resolved into a right hand circularly

polarized wave and a left hand circularly polarized waves are equal amplitude.(4)

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