AR13 Model Question Paper

Code: 13EE2006

ADITYA INSTITUTE OF TECHNOLOGY AND MANAGEMENT, TEKKALI (AUTONOMOUS)

II B.Tech. I Semester Regular Examinations, January, 2015 ELECTRO MAGNETIC FIELDS (ELECTRICAL & ELECTRONICS ENGINEERING) Time: 3 Hours

Max Marks: 70 PART – A

• Answer all questions in PART – A • Answer one question from each unit of PART-B PART-A

[1X10 = 10M]

1. Define a scalar field and vector field. 2. State coulomb's law 3. State Gauss's law 4. Define work done 5. Define relaxation time. 6. State uniqueness theorem. 7. State Biot-savart law. 8. State Ampere's circuit law. 9. Define magnetic torque. 10. State Faraday's law. PART-B

[5X12 = 60M]

UNIT-I 2. Derive an expression for electric field intensity at a distance ‘h’ along the Z-axis due to an infinite sheet of charge placed in the Z=0 plane. [12M] (OR) 3. For a physical dipole in the z-direction, located at the origin in free space, find the ∏ potential at a point ( r, (in spherical co ordinates). 2 UNIT-II 4. Derive an expression for capacitance between two concentric spherical shells. [12M] (OR)  in a uniform electric filed E  is given by 5. Show that the torque on a physical dipole P

[12M]

 P

 XE

. Extend this result to a pure dipole.

[12M]

UNIT-III 6. Find the expression for the magnetic flux density, ‘B’ at a distance ‘h’ above the centre of a square loop of wire ‘b’ meters of each side. The loop carries a current of one ampere. [12M] (OR) 7. Derive the expression for magnetic flux density at a point due to an infinitely long current carrying conductor. [12M] UNIT-IV 8. A solenoid of 10 cm in length consists of 1000 turns having the cross section radius of 1 cm. Find the inductance of solenoid. What is the value of current required to maintain a flux of 1 mWb in the toroid. Take µr = 1500. [12M] (OR) 9. A very long solenoid with 6 cm2 cross section has an iron core µr = 1000 and 400 turns/meter. If it carries a current of 500 mA, find: i) its self inductance per meter ii) the energy per meter stored in its field. [12M] UNIT-V 10. Derive the Maxwell’s equations in point and integral form for time varying fields? [12M] (OR) 11. Show that power loss in a conductor is given as product of voltage and current using Poynting theorem. [12M] ***

ELECTRO MAGNETIC FIELDS

(ELECTRICAL & ELECTRONICS ENGINEERING) Subject Code: 13EE2006 Credits: 03

External Marks: 70 Internal Marks: 30

Objective: To have knowledge in fundamentals of static electric, magnetic, dynamic electromagnetic fields and their applications,which is the backbone of electrical engineering. Outcomes: On completion of the course the student shall be able to analyse potential problems within electrostatics, magneto statics and stationary current distributions in linear, isotropic media, and also solve such problems in simple geometries.

UNIT – I Vectors Analysis: Scalar, Vector, Field, Scalar & Vector Products, Vector component, Unit vector, Unit vector normal to a plane, Vector Triple product, Co-ordinate systems- Cartesian, Cylindrical, Spherical, differential length, area, volume in these co-ordinate systems, Importance of divergence, curl, grad and Laplacian. Electrostatics: Electrostatic Fields – Coulomb’s Law – Electric Field Intensity (EFI) – EFI due to a line and a surface charge – Work done in moving a point charge in an electrostatic field – Electric Potential – Properties of potential function – Potential gradient – Guass’s law – Application of Guass’s Law – Maxwell’s first law, div( D )=ρv UNIT – II Conductors and Dipole: Laplace’s and Poison’s equations – Solution of Laplace’s equation in one variable. Electric dipole – Dipole moment – potential and EFI due to an electric dipole – Torque on an Electric dipole in an electric field – Behaviour of conductors in an electric field – Conductors and Insulators. Dielectrics & Capacitance: Electric field inside a dielectric material – polarization – Dielectric – Conductor and Dielectric – Dielectric boundary conditions, Capacitance – Capacitance of parallel plate and spherical and coaxial capacitors with composite dielectrics

UNIT – III MagnetoStatics: Static magnetic fields – Biot-Savart’s law – Oesterd’s experiment - Magnetic field intensity (MFI) – MFI due to a straight current carrying filament – MFI due to circular, square and solenoid current – Carrying wire – Relation between magnetic flux, magnetic flux density and MFI – Maxwell’s second Equation, div(B)=0. Ampere’s circuital law and its applications viz. MFI due to an infinite sheet of current and a long current carrying filament – Point form of Ampere’s circuital law – Maxwell’s third equation, Curl (H)=J, Field due to a circular loop, rectangular and square loops. UNIT IV Magnetic Forces and Magnetic Potential: Magnetic force - Moving charges in a Magnetic field – Lorentz force equation – force on a current element in a magnetic field – Force on a straight and a long current carrying conductor in a magnetic field – Force between two straight long and parallel current carrying conductors – Magnetic dipole and dipole moment – a differential current loop as a magnetic dipole – Torque on a current loop placed in a magnetic field. UNIT – V Self and Mutual Inductances: Self and Mutual inductance – Neumans’s formulae – determination of self-inductance of a solenoid and toroid and mutual inductance between a straight long wire and a square loop wire in the same plane – energy stored and density in a magnetic field. Time Varying Fields and Maxwell’s Equations: Time varying fields – Faraday’s laws of electromagnetic induction – Its integral and point forms – Maxwell’s fourth equation, Curl (E)=-∂B/∂t – Statically and Dynamically induced EMFs – Simple problems -Modification of Maxwell’s equations for time varying fields – Displacement current – Poynting Theorem and Poynting vector. TEXT BOOKS: 1.“Engineering Electromagnetics” by William H. Hayt & John. A. Buck Mc. Graw-Hill Companies, 7th Editon.2006. 2.“ Principles of Electro Magnetics” by Sadiku, Oxford Publications,4th edition. REFERENCE BOOKS 1.“Introduction to Electro Dynamics” by D J Griffiths, Prentice-Hall of India Pvt.Ltd, 2nd edition. 2. Electrical field theory by Gangadhar, Khanna publishers. 3. Electro Magnetic field theory by Edminister, TMH publishers