Rr210204 Electromagnetic Fields

Set No. 1

Code No: RR210204

II B.Tech I Semester Supplimentary Examinations, November 2007 ELECTROMAGNETIC FIELDS (Electrical & Electronic Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define the potential and potential gradient.

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(b) Derive Poisson’s and Laplace equations.

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2. (a) Two long metal plates of width 1 m each held at an angle of 100 by an insulated hinge(plates are electrically separated) using laplace’s equation determine potential function. [8] (b) Potential distributions are given by V=4/(x2 + y + z 2 ) Find the expression for E. [8] 3. (a) Derive the expression for potential and field between two co-axial cylinders. [8] (b) Find the capacitance of parallel plate capacitor when A = 1sq mt distance between the plate 1 mm voltage gradient is 105 V /m and charge density on the plate is 2 µC/m2 . [8] 4. (a) Derive the integral form of continuity equation and also write its meaning. [10] (b) What is the Capacitance of a Capacitor consisting of two parallel plates 30 cm by 30 cm, Separated by 5 mm in air. What is the energy stored by the capacitor if it is charged to a potential difference of 500 volts. [6] 5. (a) State and explain Biot-Sarvart’s Law

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(b) Derive an expression for magnetic field intensity at a radial distance R due to an infinite conductor carrying a current I. [10] 6. A current strip 2cm wide carries a current of 15 amps in the a¯x direction, as shown in ¯ = 0.20¯ figure 6. Find the force on the strip of unit length if the uniform field is B ay Tesla. [16]

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Set No. 1

Code No: RR210204

Figure 6 7. Derive formula for self-inductance of a solenoid. Use this formula and find selfinductance of a solenoid having 500 turns, mean diameter equal to 10 cm and length equal to 5 cm. Assume medium to be air. [16] 8. (a) Write down Maxwell’s equations in their general integral form. Derive the corresponding equations for fields varying harmonically with time. [10] (b) Show that the ration of the amplitude of the conduction current and displaceσ for the applied field E = Emax Cos wt V/m. [6] ment current density is ωε ⋆⋆⋆⋆⋆

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Set No. 2

Code No: RR210204

II B.Tech I Semester Supplimentary Examinations, November 2007 ELECTROMAGNETIC FIELDS (Electrical & Electronic Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Show that the electric field intensity due to an infinite sheet of charge is independent of the distance of the point from sheet [8] (b) A uniform line charge λL = 25nC/m lies on the line x = -3 and z =4 m in free space. Find the electric field intensity at a point (2,5,3)m. [8] 2. (a) State and prove Gauss’s law.

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(b) Derive and plot the electric field intensity of a spherical volume distribution of charge using Gauss’s law. [10] 3. (a) Derive the expression for capacitance of the spherical condensor.

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(b) The radii of two spheres differ by 4 cm and the capacitance of the spherical condensers is 53.33 pf. If the outer sphere is earthed, calculate the radii assuming air as dielectric [8] 4. The parallel plate capacitor with a flat slab of dielectric material between the ¯ plates shown in below figure 4. Assuming top plate as the charged, calculate D and P¯ [16]

Figure 4 5. A conductor is in the form of a Regular polygon of n sides inscribed in a circle of radius R. Show that  the expression for B at the center for a current is given by I |B| = nµo /2πR T an π/n [16] 6. A steady current of 1000A is established in a long straight, hollow aluminium conductor of inner radius 1cm and outer radius 2 cm. Assume uniform resistively and calculate B as a function of radius r from the axis of the conductor. [16] 7. Current in a coil is increased from zero to 10 Amps at a uniform rate is 5 seconds. It is found that the coil develops self-induced e.m.f. of 100 volts where as an e.m.f. of 20 volts in produced in a neighbouring coil. Compute self-inductance of the first coil and mutual inductance between the two coils. [16] 1 of 2

Set No. 2

Code No: RR210204

8. (a) Starting form first principle derive Maxwell’s equation using Faraday’s law and show that div B=0. [8] (b) For coaxial cylindrical condenser of radii ‘a’ and ‘b’ length ‘L’, evaluate the total displacement current flowing across any cylindrical surface of radius ‘r’ (a < r < b), taking the average variation as sinusoidal in time and the variation of electric field with radius the same as in statics. Show that the result is independent of radius and equal to the charging current for the condenser.[8] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: RR210204

II B.Tech I Semester Supplimentary Examinations, November 2007 ELECTROMAGNETIC FIELDS (Electrical & Electronic Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. An infinitely large cylinder has a radius and a uniform charge of one micro coulomb per meter. Calculate the potential at a point 10m away from the cyclinder if zero potential point is taken to be at a radial distance of 1m. [16] 2. (a) If a sphere of radius ‘a’ has a charge density ρ = kr3 Find D and ∇.D as a function of radius and sketch the results. k is a constant. [6] (b) A charge Q is uniformly distributed in a half-circular ring of radius ‘a’. Determine E at center. [10] 3. (a) A co axial cable with inner and outer conductor radii ‘a’ and ‘b’ respectively have the respective voltage Va and Vb. By using laplace?s equation, find E at all points. [10] (b) The construction of a paper capacitor is as follows: Aluminum foil of 100−cm2 area is placed on both sides of paper of thickness 0.03 mm. If the dielectric constant of paper is given as 3, and its dielectric breakdown strength is 200 kV/cm , what is the rating of the capacitor? [6] 4. (a) Derive the integral form of continuity equation and also write its meaning. [10] (b) What is the Capacitance of a Capacitor consisting of two parallel plates 30 cm by 30 cm, Separated by 5 mm in air. What is the energy stored by the capacitor if it is charged to a potential difference of 500 volts. [6] 5. A conductor is in the form of a Regular polygon of n sides inscribed in a circle of radius R. Show that  the expression for B at the center for a current is given by I |B| = nµo /2πR T an π/n [16] 6. A single-phase circuit comprises two parallel conductors A and B, each 1 cm diameter and spaced 1 m apart. The conductors carry current of +100 and -100 Amps. respectively. Determine the filed intensity at the surface of each conductor and also in space exactly midway between A and B. [16] 7. Compute energy density in free space on account of field having H = 1000 A/mt. Derive formula used. [16] 8. Write the Maxwell’s equations in free space. ⋆⋆⋆⋆⋆

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Set No. 4

Code No: RR210204

II B.Tech I Semester Supplimentary Examinations, November 2007 ELECTROMAGNETIC FIELDS (Electrical & Electronic Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Determine the potential along the axis of a uniformly charged disc of radius ‘a’. The centre of the disc coincides with the origin and the disc is in x-y plane. Also find electric field on the axis [8] (b) A charge of 8nC is distributed uniformly along a line of length 8m. Find the field intensity at a radial distance of 2m from the center of the line, assuming air medium [8] 2. (a) Two long metal plates of width 1 m each held at an angle of 100 by an insulated hinge(plates are electrically separated) using laplace’s equation determine potential function. [8] (b) Potential distributions are given by V=4/(x2 + y + z 2 ) Find the expression for E. [8] 3. (a) Calculate the capacitance of a parallel plate capacitor with following details. Plate area = 100 sq.cm. Dielectric ǫr1 = 4, d12 = 2mm Dielectric ǫr2 = 3, d12 = 3 mm If 200 V is applied caross the plates what will be the voltage gradient across each dielectric. [8] (b) The permitivity of the dielectric of parallel plate capacitor increases uniformly from ǫ1 at one plate to ǫ2 at the other. If A is the surface areas of the plate and d is the thickness of dielectric, derive an expression for capacitance. [8] 4. (a) Three point charges 1nC, 3nC and 4nC are located (0,0,0),(0,0,1) and (1,0,0) respectively. Find the energy in the system. [8] (b) Find the expression for the energy per unit volume of the dielectric due to electric field in a charged capacitor. [8] 5. State and prove Ampere’s circuital law. Discuss few applications for the same.[16] 6. Derive an expression for force between two straight long parallel current carrying conductors. What will be the nature of force if the current are in the same and opposite direction? [16] 7. A solenoid of 500 turns has a length of 50 cm and radius of 10 cm. A steel rod of circular cross section is fitted in the solenoid co-axially and tightly. Relative permeability of steel is 3000. A d.c. Current of 10 Amps is passed through the solenoid. Compute inductance of the system, energy stored in the system and mean flux density inside the solenoid. [16] 1 of 2

Set No. 4

Code No: RR210204

8. Write Maxwell’s equations in good conductors for time varying fields and static fields both in differential and integral form? [16] ⋆⋆⋆⋆⋆

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