**B.Tech.** **(EE-2011 Batch)**

## Electromagnetic Fields

### Subject Code : BTEE-403Â Â Â Â Â Â Paper ID : [ A1206]

### Time : 3 Hrs.Â Â Â Â Â Â Â Â Â Â Â Â Â Max. Marks : 60

#### INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.

2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.

3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions

## Electromagnetic Fields 4th Sem B.Tech PTU Nov 2018 Question Paper **SECTION-A**

**Q1. Write Briefly**

#### Â Â a) Find a vector normal to a plane consisting of points pl(0,l,0), p2(l,0,l) and p3(0,0,l).

#### Â Â b) State Stokes theorem.

#### Â Â c) State and explain the relationship between potential gradient and electric field.

#### Â Â d) What are the sources of electric field and magnetic field?

#### Â Â e) Explain a few applications of Gauss law in electrostatics.

#### Â Â f) State and explain Biot -Savarts law.

#### Â Â g) What is a dipole? Calculate the dipole moment of a dipole with charges 2C and -2C separated by a distance of 2cm.

#### Â Â h) What is capacitance? Calculate the capacitance of a air filled capacitor having two parallel plates of area 2m2 separated by a distance of 0.2m.

Â Â i) Calculate the emf of a material having a flux linkage of 2t2 at time t = 1 second.

Â Â j) What is phase constant? Calculate the velocity of wave propagation in a conductor with frequency 5 Ã— 108 rad/s and phase constant of 3 Ã— 108 units.

## Â **Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SECTION-B**

**Q2. Attempt any five questions.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5×6=30**

#### Â Â Â Q2. State and explain Ampereâ€™s law and modified Ampereâ€™s law. A solid cylindrical conductor of radius R has a uniform current density. Derive expression for H for both inside and outside of the conductor. Plot the approximate variation of H as a function of radial distance from the centre of wire.

#### Â Â Â Q3.What do you understand by Gradient and Curl? Find the gradient of the function given by *x*^{2}+*y*^{2}+*z*^{2} at (1, 1, 1). Find the curl of the gradient vector as obtained for the above function.

#### Â Â Â Q4. A uniform plane electromagnetic wave with field varying sinusoidally with time, in medium â€˜Aâ€™ is incident normally on the surface of medium â€˜Bâ€™ Derive the expression for the reflection and refraction coefficients.

#### Â Â Â Q5. What is magnetic field intensity? The positive y axis (semi-infinite line w.r.t. the origin) carries a filamentary current of 2 A in the – direction. Assume it is a part of a large circuit. Find magnetic field intensity at (2, 3, 0).

#### Â Â Â Q6. What is the significance of the Maxwellâ€™s equations? State the Maxwellâ€™s equations in integral form for static and time varying fields.

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SECTION-C**

**Q3. Attempt any three questions.****Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3×10=30**

#### Â Â Q7. State and explain Ampereâ€™s law and modified Ampereâ€™s law. A solid cylindrical conductor of radius R has a uniform current density. Derive expression for H for both inside and outside of the conductor. Plot the approximate variation of H as a function of radial distance from the centre of wire.

Â Â Q8. Explain Poynting Vector. A plane electromagnetic wave having a frequency of 10 MHz has an average Poynting vector of 1 W/m2. If the medium is lossless with relative permeability of 2 and relative permittivity of 3 Find :

Â Â Â a) The velocity of propagation,

Â Â Â b) The wavelength,

Â Â Â c) The impedance of the medium,

Â Â Â d) The rms value of the electric field E.

#### Â Q9. Write a short note on the following :

Â Â a) Greenâ€™s theorem

Â Â b) Continuity equation

Â Â c) Analogies between electric and magnetic fields

Â Â d) Polarization

#### Find a vector normal to a plane consisting of points pl(0,l,0), p2(l,0,l) and p3(0,0,l).

#### Â

#### Â Stokes theorem.

#### Â

#### Explain the relationship between potential gradient and electric field.

#### Â

#### Sources of electric field and magnetic field

#### Â

#### Applications of Gauss law in electrostatics.

#### Â

#### Explain Biot -Savarts law.

#### Â

#### Dipole

#### Calculate the dipole moment of a dipole with charges 2C and -2C separated by a distance of 2cm.

#### Â

#### Capacitance

#### Calculate the capacitance of a air filled capacitor having two parallel plates of area 2m2 separated by a distance of 0.2m.

#### Find emf of a material having a flux linkage of 2t2 at time t = 1 second.

#### Phase constant

#### Calculate the velocity of wave propagation in a conductor with frequency 5 Ã— 108 rad/s and phase constant of 3 Ã— 108 units.

##### Electrical Engg.Materials EE-208 4th Sem NOV 2018 B.Tech EE PaperÂ

#### Explain Ampereâ€™s law and modified Ampereâ€™s law.

#### A solid cylindrical conductor of radius *R *has a uniform current density.

#### Derive expression for *H *for both inside and outside of the conductor. Plot the approximate variation of H as a function of radial distance from the centre of wire.

#### Gradient and Curl? Find the gradient of the function given by *x*^{2}+*y*^{2}+*z*^{2} at (1, 1, 1).

#### Find the curl of the gradient vector as obtained for the above function.

#### Â

#### uniform plane electromagnetic wave with field varying sinusoidally with time, in medium â€˜Aâ€™ is incident normally on the surface of medium â€˜Bâ€™ Derive the expression for the reflection and refraction coefficients.

#### Magnetic field intensity

#### The positive y axis (semi-infinite line w.r.t. the origin) carries a filamentary current of 2 A in the – direction. Assume it is a part of a large circuit. Find magnetic field intensity at (2, 3, 0).

#### Significance of the Maxwellâ€™s equations

#### State the Maxwellâ€™s equations in integral form for static and time varying fields.

##### Electromagnetic Fields 4th Sem B.Tech PTU Nov 2018 Question PaperÂ

#### Explain Ampereâ€™s law and modified Ampereâ€™s law.

#### A solid cylindrical conductor of radius R has a uniform current density.

#### Derive expression for H for both inside and outside of the conductor. Plot the approximate variation of H as a function of radial distance from the centre of wire.

#### Poynting Vector.

#### A plane electromagnetic wave having a frequency of 10 MHz has an average Poynting vector of 1 W/m2. If the medium is lossless with relative permeability of 2 and relative permittivity of 3 Find :

#### a) The velocity of propagation,

b) The wavelength,

c) The impedance of the medium,

d) The rms value of the electric field E.

#### Â

#### Short note on the following :

a) Greenâ€™s theorem

#### Short Note on b) Continuity equation

#### Short Note on c) Analogies between electric and magnetic fields

#### A Short Note on d) Polarization

##### Electromagnetic Fields 4th Sem B.Tech PTU Nov 2018 Question Paper

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