EMT Solved Semester Question Paper 2019 Dec (2017 Reg)

DECEMBER - 2019

Electromagnetic Theory (90198)

Solved Paper

Sem – III [EEE]

Regulation 2017

Time : Three Hours]

PART A - (10 × 2 = 20 Marks)

Q. 1 State Coulombs law. (Refer Two Marks Q.l of Chapter - 2)

Q. 2 Given vector field . Find this vector field at P(2, 3, 1) and its projection on

.(Refer Two Marks Q.56 of Chapter - 1)

Q.3 How is electric energy stored in a capacitor ? (Refer Two Marks Q.42 of Chapter - 5)

Q.4 What are equipotential surfaces 1 (Refer Two Marks Q.6 of Chapter - 4)

Q.5    Write down the expression for magnetic field at the centre of the circular coil.

(Refer Two Marks Q.31 of Chapter - 7)

Q.6 What is energy density in magnetic field ? (Refer Two Marks Q.41 of Chapter - 8)

Q.7 Mention the significance of displacement current. (Refer Two Marks Q.8 of Chapter - 9)

Q.8 State Maxwell's fourth equation. (Refer Two Marks Q.39 of Chapter - 9)

Q.9 What will happen when the wave is incident obliquely over dielectric-dielectric boundary ?

(Refer Two Marks Q.67 of Chapter - 10)

Q.10 Define skin depth. (Refer Two Marks Q.21 of Chapter - 10)

PART B - (5 × 13 = 65 Marks)

Q.11 a) Calculate the line integral of the vector field  along the following two paths joining the origin to the point P(l, 1, 1). (Refer example 4.3.5)

i) Along a straight line joining the origin to P.

ii) Along a path parameterized by x = t, y = t² ,z = t³.

From the result of this problem, can you conclude that the force is conservative ? If so, determine a potential function for this vector field.

OR

b) Calculate the flux of the vector field over the surface of a unit cube whose edges are parallel to the axes and one of the corners is at the origin. Use this result to illustrate the divergence theorem.

(Refer example 1.16.1)

Q.12 a) Find electric field due to a charged ring on its axis. (Refer section 2.7)

OR

b) If ϕ (r, θ, ϕ satisfies Laplace's equation inside a sphere, show that the average of ϕ (r, θ, ϕ) over the surface is equal to the value of the potential at the origin. (Refer example 4.8.3)

Q.13 a) A long cylindrical wire has a current density flowing in the direction of its length whose density is J = J Q r , where r is the distance from the cylinder's axis. Find the magnetic field both inside and outside the cylinder.

(Refer example 7.9.4)

OR

b) Derive vector potential for a uniform magnetic field. (Refer section 7.12.3)

Q.14 a) A charge q is moving with a uniform velocity  Obtain its Poynting vector and show that the energy propagates along with the moving charge. (Refer section 10.8)

OR

b) A conductor 1 m in length is parallel to z-axis and rotates at radius of 25 cm at 1200 rpm. Find induced voltage, if the radial field is given by . (Refer example 9.2.7) 

Q.15 a) Discuss the propagation of electromagnetic wave at the interface between two dielectric media. (Refer section 10.10)

OR

b) A circularly polarized electromagnetic wave is given by :

Show that the average value of the Poynting vector for the wave is qual to the sum of the poynting vectors of its components. (Refer example 10.8.5)

PART C - (1 × 15 = 15 Marks)

Q.16 a) A square loop of side a lies in the xy plane, as shown.

A magnetic field exists in the region directed along the z direction and varies with time and space as

 where B₀ is appropriately dimensioned.

Calculate the emf developed in the loop. If the x component of the induced electric field is zero, obtain an expression for the electric field induced and show that the line integral of the electric field correctly gives the emf calculated. (Refer example 9.2.11)

OR

b) Obtain an expression for the Laplacian operator in the cylindrical coordinates. (Refer example 6.2.5)