NSCET Department of ECE YR/QB/EC6403-EMF QB.pdf · 6.2 Derive point form of Ampere‟s circuital law L4 Analysis 2 6.3 A current of 3mA flowing through an inductor of 100mH.What is

NSCET Department of ECE

Electromagnetic Field Page 1

SEM- 4th

Semester – B.E.

BR- Department of Electronics and Communication Engineering

Part-A (10 x 2 = 20 Marks)

UNIT – I STATIC ELECTRIC FIELD

No Question Level Competence Mark

1.1 Define line charge density. Write its unit L1 Remember 2

1.2 Find the electric field intensity E at (1, 1,1) if the

potential is V = x y z2 + x

2 y z + x y

2 z (V).

L5 Evaluation 2

1.3 State Divergence theorem. L1 Remember 2

1.4 Define gradient of a scalar field L1 Remember 2

1.5 State coulombs law L1 Remember 2

2.1 Write the equation for Gauss law. L4 Analysis 2

2.2 State Gauss law and write its applications. L3 Application 2

2.3 Define electric dipole. L1 Remember 2

2.4 State Stoke‟s theorem. L1 Remember 2

2.5 What is an electric potential? Write expression for

potential due to an electric dipole.

L2 Understand 2

Nadar Saraswathi College of Engineering and Technology,

Vadapudupatti, Theni - 625 531

(Approved by AICTE, New Delhi and Affiliated to Anna University, Chennai)

Format No. NAC/TLP-

07a.12

Rev. No. 01

Date 14-11-2017

Total Pages 12

Question Bank for the Units – I to V



UNIT – II CONDUCTORS AND DIELECTRICS

3.1 Define current density at a given point. L1 Remember 2

3.2 Write the boundary conditions for electric field at

perfect dielectric conductor interface?

L2 Understand 2

3.3 Write Laplace‟s equations in all the three coordinates. L4 Analysis 2

3.4 Write the equation for energy stored in electrostatic

field in terms of field quantities.

L4 Analysis 2

3.5 Define resistance of a conductor L1 Remember 2

4.1 Write the relation between perfect conductor and

electrostatic field

L2 Understand

2

4.2 Find the energy stored in the 20 pF parallel plate

capacitor with plate separation of 2 cm. The

magnitude of electric field in the capacitor is 1000 V /

m.

L5 Evaluation

2

4.3 What is dielectric polarization? L2 Understand 2

4.4 What is the practical application of method of

images?

L3 Application

2

4.5 Give Laplace‟s and Poisson‟s equations. L4 Analysis 2

UNIT – III STATIC MAGNETIC FIELDS

5.1 Define magnetic scalar potential L1 Remember 2

5.2 State Biot - Savart law L1 Remember 2

5.3 Define magnetic vector and scalar potential. L1 Remember 2

5.4 Define capacitance and capacitor L2 Understand 2

5.5 State ampere‟s circuital law. L1 Remember 2



6.1 Write the relation between magnetic flux and

magnetic flux density

L2 Understand 2

6.2 Derive point form of Ampere‟s circuital law L4 Analysis 2

6.3 A current of 3mA flowing through an inductor of

100mH.What is the energy stored in inductor?

L5 Evaluation 2

6.4 An infinitesimal length of wire is located at (1, 0, 0)

and carries a current 2A in the direction of unit vector

az. Find the magnetic flux density due to the current

element at the field point (0, 0, 2).

L5 Evaluation

2

6.5 What is vector magnetic potential? L2 Understand 2

UNIT-IV MAGNETIC FORCES AND MATERIALS

7.1 Write an expression for torque in vector form L4 Analysis 2

7.2 In a ferromagnetic material (µ= 4.5 µo), the magnetic

flux density is B=10 y ax m Wb / m2. Calculate the

magnetization vector.

L5 Evaluation 2

7.3 Mention the force between two current elements. L2 Understand 2

7.4 Define skin depth L1 Remember 2

7.5 Calculate the mutual inductance of two inductively

tightly coupled coils with self-inductance of 25mH

and 100mH.

L5 Evaluation 2

8.1 Write the expressions for energy stored in magnetic

field

L4 Analysis

2

8.2 What is the energy stored in a magnetic field in terms

of field quantities?

L2 Understand

2

8.3 Differentiate diamagnetic, paramagnetic and

ferromagnetic material.

L2 Understand

2

8.4 Define dielectric strength L1 Remember 2



8.5 Give the expression for Lorentz force equation L4 Analysis 2

UNIT- V TIME VARYING FIELDS AND MAXWELL’S EQUATIONS

9.1 State Faraday‟s law for a moving charge in a constant

magnetic field

L2 Understand

2

9.2 What are the Maxwell‟s equations for free space

medium?

L2 Understand 2

9.3 State Faraday‟s law of induction. L1 Remember 2

9.4 Differentiate conduction current and displacement

current.

L2 Understand

2

9.5 Define phase velocity L1 Remember 2

10.1 State poynting theorem. L1 Remember 2

10.2 In a medium, the electric flux intensity is E= 10 sin

(1000 t - 10 x) ay V/m. Calculate the displacement

current density (𝜀r= 80)

L5 Evaluation

2

10.3 What is poynting vector? L4 Analysis 2

10.4 List any two properties of uniform waves. L2 Understand 2

10.5 Find displacement current density for field E = 300

sin 109t V / m.

L5 Evaluation 2

Part – B ( 5 x 16 = 80 Marks) or Part – B ( 5 x 13 = 65 Marks)

UNIT- I STATIC ELECTRIC FIELD

11.a-1 Given D = 2 r z2 ar + r cos

2 az. prove divergence

theorem

L6

Create

(13)



11.a-2 Define the potential difference and electric field. Give

the relation between potential and field intensity. Also

derive an expression for potential due to infinite

uniformly charged line and also derive potential due to

electric dipole.

L4

Analysis

(13)

11.a-3 i) State and prove stokes theorem.

ii) Derive the expression for energy and energy

density in static electric fields.

L1

L2

Remember

Understand

(8)

(5)

11.a-4 i)State and explain Divergence theorem

ii) Determine the electric flux density D at ( 1, 0, 2) if

there is a point charge 10mC at (1, 0, 0) and a line

charge of 50mC/ m along y axis.

L1

L5

Remember

Evaluation (7)

(6)

11.b-1 i) Using gauss law find the electric field intensity for

the uniformly charged sphere of radius „ a‟ find the E

everywhere.

ii) Derive the equation for scalar electric potential

L2

L4

Understand

Analysis

(8)

(5)

11.b-2 i) State and prove Gauss law and explain any one of

applications of Gauss law.

ii)Given two vectors 𝑨 =3 ax + 4 ay – 5 az and 𝑩 = - 6

ax + 2 ay – 45 az, determine the unit vector normal to

the plane containing the vectors 𝑨 and 𝑩

L2

L4

Understand

Analysis

(7)

(6)

11.b-3 i) A circular disc of radius „a‟ meter is charged

uniformly with a charge of 𝜌 c / m. Find the electric

field intensity at appoint h meter from the disc along

its axis.

ii) Explain the concept of superposition principle of

electric field intensity.

L2

L1

Understand

Remember

(8)

(5)

11.b-4 i) The two point charges 10 µC and 2 µC are located (6)



at (1, 0, 5) and (1, 1,0) respectively. Find the potential

at (1, 0,1) assuming zero potential at infinity.

ii) What maximum charge can be put on a sphere of

radius 1m, if the breakdown of air is to be avoided?

For break down of air, E= 3 x 106 V/m

L6

L5

Create

Evaluation

(7)


12.a-1 Derive an expression for capacitance of a coaxial

cable.

(OR)

Find the capacitance for a coaxial capacitor with

inner radius „a‟ and outer radius „b‟ with length L

L2

Understand

(13)

12.a-2 i) Derive the relationship between polarization and

electric field intensity.

ii) Derive the capacitance of a spherical capacitor.

L

L2

Understand

(7)

(6)

12.a-3 i) Derive the expression for relaxation time by

solving the continuity equation.

ii)Calculate the relaxation time of mica (𝜍 = 10 -15

S /

m, 𝜀t = 6) and paper (𝜍 = 10 -11

S / m, 𝜀r = 7)

L4

L5

Analysis

Evaluation

(8)

(5)

12.b-1 Derive the boundary condition for the E-field and H-

field in the interference between dielectric and free

space.

L2 Understand (13)

12.b-2 i)Derive the Poison‟s equation

ii) A spherical capacitor consists of an inner

conducting sphere of radius „a‟ and an outer

conductor with spherical inner wall of radius is „b‟.

The space between the conductors is filled with a

dielectric permittivity „𝜀‟. Determine the capacitance.

L4 Analysis (5)

(8)

12.b-3 i) Derive Laplace‟s equations

ii) If two parallel plates of area 4 m2 are separated by

a distance 6 mm, find the capacitance between these

2 plates. if a rubber sheet of 4 mm thickness with 𝜀r

= 2.4 is introduced between the plates leaving a gap

L4 Analysis (7)



of 1mm on both sides, determine the capacitance (6)


13.a-1 State Biot- Savart‟s law. Derive the expressions for

magnetic field intensity and magnetic flux density at

the centre of the square current loop of side l. Then

determine the same for square loop of sides 5 m

carrying current of 10 A.

L2,

L5

Remember,

Evaluation

(13)

13.a-2 From Biot Savart‟s law obtain expression for

magnetic field intensity and vector potential at a

point P and distance „R‟ from infinitely long straight

current carrying conductor.

L2

Understand (13)

13.a-3 An infinitely long, straight conductor with a circular

cross section of radius „b‟ carries a steady current I.

Determine magnetic flux density both inside and

outside the conductor.

(OR)

Derive an expression for magnetic field due to an

infinitely long coaxial cable

L4

Analysis

(13)

13.b-1 i) consider two identical circular current loops of

radius 3 m and opposite current 20 A are in parallel

planes, separated on their common axis by 10 m.

Find the magnetic field intensity at a point midway

between the two loops.

ii) State Biot-Savart‟s law. Find the magnetic field

intensity at the origin due to current element

I 𝑑𝑙 = 3𝜋 (ax + 2 ay + 3 az ) 𝜇 A.m at (3, 4, 5) in free

space.

L6

Create

(8)

(5)



13.b-2 i) Derive the expression for vector magnetic potential

interms of current density.

ii) For a current distribution in free space,

A = (2 x2y + yz) ax + (xy

2- zx

3) ay –(6xyz – 2x

2y

2) az

Wb/m. Calculate magnetic flux density.

L4

L5

Analysis

Evaluation

(8)

(5)

13.b-3 Determine H at (0, 0, 4) and (0, 0,-4) for a circular

loop located on X2 + Y

2 =9, Z=0 carries a direct

current of 10A along a∅.

ii)Obtain the expression for magnetic field intensity

at the centre of the circular wire

L5

L4

Evaluation

Analysis

(8)

(5)

UNIT –IV MAGNETIC FORCES AND MATERIALS

14.a-1 i) Derive the equation to find the force between the

two current elements.

ii) Derive the equation for the magnetization for the

materials and show that J b = 𝛁 × 𝒎 and

Kb = m × an .

L4

Analysis

(7)

(6)

14.a-2 i) Derive the expression for force on a moving charge

in a magnetic field and Lorentz force equation.

ii) Derive the inductance of a toroid.

L4

Analysis

(7)

(6)

14.a-3 i) A charged particle with velocity 𝑢 is moving in a

medium containing uniform field 𝐸 = E ax V / m and

𝐵 = B ay Wb / m2. What should 𝑢 be so that the

particle experiences no net force on it?

ii) State and derive the magnetic boundary conditions

between the two magnetic mediums.

L5

L4

Evaluation

Analysis

(7)

(6)

14.a-4 i) Explain about magnetization vector and derive the

expression for relative permeability. L4

Analysis

(8)



ii) State and explain Ampere‟s force law. (5)

14.b-1 i) Derive an expression for inductance of a solenoid.

Calculate the inductance of solenoid, 8 cm in length,

2 cm in radius, having 𝜇r= 100 and 100 turns. (7)

ii) Give the comparison between magnetic and

electric circuits

L5

L2

Evaluation

Understand

(7)

(6)

14.b-2 Derive the expression for inductance and magnetic

flux density inside the solenoid. Calculate the

inductance of the solenoid and energy stored when a

current of 8 A flowing through the solenoid of 2 m

long, 10 cm diameter and 4000 turns.

L5

Evaluation

(13)

14.b-3 Derive the boundary conditions of static magnetic

field at the interface of two different magnetic

medium

L4

Analysis

(13)

14.b-4 i) Classify the materials based on magnetic

properties.

ii) 𝐴 = − 𝜌2/ 4 az Wb/m, calculate the total magnetic

flux crossing the surface 𝜑 = π/2, 1≤ 𝜌 ≤2m,

0 ≤ z ≤ 5m.

L2

L5

Understand

Evaluation

(6)

(7)


15.a-1 From the basic laws derive the time varying

Maxwell‟s equation and explain the significance of

each equation in detail.

L4

Analysis

(13)

15.a-2 Starting from Maxwell‟s equation derive the equation

for E field in the form of wave in free space.

(Or)

Derive the wave equation stating from Maxwell‟s

L4

Analysis

(13)



equation for free space

15.a-3 Derive the Maxwell‟s equation in differential and

integral form.

L4

Analysis

(13)

15.b-1 i) State and derive poynting theorem.

ii) Explain the transformer emf using faraday‟s law. L2 Understand

(8)

(5)

15.b-2 Explain the condition and propagation of uniform

plane waves in good conductor and derive the wave

constants.

L2 Understand (13)

15.b-3 Starting from Maxwell‟s equation, derive

homogeneous vector Helmholtz‟s equation in phasor

form

L4

Analysis

(6) (7)

Part – C ( 1 x 15 = 15 Marks)

UNIT- I STATIC ELECTRIC FIELD

16 .a-1 With relevant examples explain in detail the practical

application of electromagnetic fields.

L3 Application (15)

16 .a-2 D = 0.3 r2 ar nC/m

2 in free space a) Find E at point

P(2,25o,90

o); b) find the total charge within sphere

r=3; c) find the total electric flux leaving the sphere

r=4.

L6 Create

(15)

(OR)

16.b-1 i) A charge +Q located at A(-a,0,0) and another

charge -2Q located at B(a,0,0).Show that the neutral

point also lies on the x- axis, where x= -5.83a.

ii) Derive coulomb‟s law starting from Gauss

theorem. State any reasonable assumptions which you

think are necessary for the derivation

L6

L4

Create

Analysis

(8)

(7)



16.b-2 i) The potential V=10 sin𝜃 cos ∅/ r2 find electric flux

density D at (2, π/2, 0)

ii) Transform A=yax+xay+x2(x

2+y

2)

-1/2az from Cartesian to

Cylindrical

L5

L6

Evaluation

Create

(7)

(8)


16 .a-1 Determine whether or not the following potential fields

satisfy the Laplace‟s equation

a) V= x2 - y2 + z

2.

b) V= r cos∅ + z.

c) V = r cos 𝜃 + ∅ .

L5 Evaluation

15

16 .a-2 i) If J= (2 cos𝜃 ar + sin cos𝜃 a𝜽)/ r3 A/m

2, Calculate the

current through a) a hemispherical shell of radius 20 cm

b)A spherical shell of radius 10 cm.

ii) A Wire of radii 0.5 mm and conductivity 5 x 107 S/m has

1029

free electrons/m3.when an E 10 mV/m is applied. Find

the charge density of free electrons, current density and

current in the wire.

L6 Create

15

(OR)

16.b-1 Explain the application of Poisson‟s equation and Laplace‟s

equation L3

Application

(15)

16.b-2 A capacitor of capacitance C is charged to a voltage V.

At a particular time, this capacitor is connected to a

second capacitor also of value C, but containing no

charge. What will be the final voltage?

L5 Evaluation

15


16 .a-1 Find the magnetic field of current in a straight circular

cylindrical conductor of radius “a” and express the

magnetic field as a vector in terms of current density.

L4 Analysis

15

16 .a-2 Determine H at (0, 0, 4) and (0, 0,-4) for a circular loop

located on X2 + Y

2 =9, Z=0 carries a direct current of

10A along a∅.

L5 Evaluation

15

(OR)

16.b-1 Derive the Biot-Savart law & Ampere‟s circuit law by using

magnetic vector potential. L4 Analysis

15



16.b-2 Derive Magnetic scalar & vector potentials L4

Analysis 15

UNIT –IV MAGNETIC FORCES AND MATERIALS

16 .a-1 i) Find the expression of induction for the co-axial.

ii) Propose the salient points to be noted when the

boundary conditions are applied.

L4

Analysis

(8)

(7)

16 .a-2 A rectangular loop carrying current I2 is placed parallel to an

infinitely long wire carrying current I1 shown in figure. Find

the force experienced by the loop.

L5

Evaluation

15

(OR)

16.b-1 A composite conductor of cylindrical cross section used

in overhead lines is made of a steel inner wire of radius

Ri and an annular outer conductor of radius Ro, the two

having electrical contact . Find the magnetic field within

the conductors and the internal self inductance per unit

length of the composite conductor.

L6

Create

(15)

16.b-2 i) Explain about magnetic Torque & Moment

ii) Derive the expression for magnetic energy L2 Remember (8)

(7)


16 .a-1 In air E= 𝑆𝑖𝑛𝜃

𝑟 cos(6 x 10

7 t – β r) a𝝋 V/m Find β and H. L6 Create

15

16 .a-2 In a medium characterized by 𝜍 =0 ,µ = µ0 , 𝜀0, and

E = 20 sin (108

t – β z) ay V/m calculate β and H. L6 Create 15

(OR)

16.b-1 In a non magnetic medium

E = 4 sin ( 2π * 107 t – 0.8 x) az V/m. Find

L6 Create 15

I

1

I

2

R

0

a

b

R



a) 𝜀r , 𝜂

b) The time average power carried by the wave

c) The total power crossing 100 cm2 of plane

2x + y =5

16.b-2 Derive the expression for total power flow in coaxial

cable. L4 Analysis 15

L1: Knowledge/Remember, L2: Comprehension/Understand, L3: Application, L4: Analysis,

L5: Evaluation, L6: Synthesis/ Create

QUESTION BANK SUMMARY

S.NO UNIT DETAILS L1 L2 L3 L4 L5 L6 TOTAL

1 Unit-1

PART-A 6 1 1 1 1 10

PART-B 3 5 3 2 2 15

PART-C 1 1 1 3 07

2 Unit-2

PART-A 2 3 1 3 1 10

PART-B 3 3 1 07

PART-C 1 2 1 04

3 Unit-3

PART-A 4 3 1 2 10

PART-B 2 2 2 1 07

PART-C 3 1 04

4 Unit-4

PART-A 2 3 3 2 10

PART-B 2 5 4 11

PART-C 1 1 1 1 04

5 Unit-5

PART-A 3 4 1 2 10

PART-B 2 4 06

PART-C 1 3 04

Total No of Questions

PART-A PART-B PART-C TOTAL

50 34 20 104



Prepared By:

Staff Name: Mr.S.Aruloli

STAFF IN CHARGE HOD PRINCIPAL

Documents

NSCET Department of ECE YR/QB/EC6403-EMF QB.pdf · 6.2 Derive point form of Ampere‟s circuital law L4 Analysis 2 6.3 A current of 3mA flowing through an inductor of 100mH.What is