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GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY Electromagnetic Field Theory (4th Semester) QUESTION BANK (Based on Numericals) 1. A boundary exists at z=0 between two dielectrics, ππ1 =2.5 region z<0 and ππ2 =4 region z>0. The field in region ππ1 is πΈβ1 = −30π₯Μ50π¦Μ + 70π§Μ V/m Find (a) Normal component of πΈβ1 (b) Tangential component of πΈβ1 (c) The angle πΌ1 <=90 degree between πΈβ1 and normal to surface (d) Normal component of π·2 (e) Tangential component of π·2 (f) Polarization in ππ2 material (g) The angle πΌ2 between πΈβ2 and normal to surface. 2. A circular line charge of density ππ C/m of radius ‘a’ is lying in XY plane with its centre at origin. Calculate the potential at point (0,0,h). 3. Three point charges 3C, 4C and 5C are situated in free space at three corners of an equilateral triangle with side 5cm. Find the energy density due to electric field in the triangle. 4. A dielectric sphere of radius ‘b’ and permittivity ‘π’ is situated in vaccum. It is charged throughout its volume by a charge density ππ£ = 5 π⁄π , ‘r’ being the distance from the centre of sphere. Determine the electrostatic energy of the system. Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY 5. For the configuration of figure, find V and E for π < π < πΌ using Laplace’s equation. Hence find the capacitance of the system. 6. Find the potential that give rise to πΈβ = 2π₯π¦ π₯Μ+π₯ 2 π¦Μ-π§Μ . 7. Given cylindrical electric fields Find the potential difference ππ΄π΅ for A(1,0,0) and B(4,0,0). 8. Given a field Calculate ππ΄π΅ for A(-5,2,1) and B(6,1,2). 9. Calculate the field due to a line charge considering it a special Gaussian surface. (keep it along z-axis) 10. A circular disk r<= 2m, in the z =0 plane has a charge density ρs = 10-8 c/ m2. Determine the electric field πΈβ at (0, Ο, h) . 11.Calculate the capacitance between concentric metal spheres of radius π1 and π2 with charge Q placed at the outer surface of inner shell. 12.State and derive the Pointing Theorem. 13.Explain briefly the term Polarisation. 14.Current density in a certain region is given by (a) Find the total current crossing the surface z=3, r<6, in π§Μ direction. (b) Find πππ£ ππ‘ Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (c) Calculate the total current crossing the closed surface bounded by z=0, z=3, r=1, r=6. (d) Is ? 15.A current of 25A passes down z-axis, enters a thin shell of radius 6cm and π = π 2 enters a plane sheet as in figure. Write expressions for the current densities in spherical shell and in plane. 16.The potential field at any point in a space containing a dielectric material of relative permittivity 2.1 is given by Where x,y,z are in meters. Calculate the volume charge density at point P(2,5,3). 17.A charge distribution with spherical symmetry has volume charge density Calculate: (a) The electric field intensity at all the points (b) Potential at all the points (c) Total energy stored in electrostatic field. 18.Given a current density Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY π in spherical coordinates. Find the current crossing the conical strip, π = , 4 0.001≤r≤0.080m. 19.Find the potential and electric field intensity for region between two concentric right circular cylinders, where v=0 at ππ =1mm and V=100V at ππ =20mm. Neglect the fringing. 20.A point charge π1 =300ππΆ located at (1,-1,-3)m experiences a force due to a point charge π2 at (3,-3,-2)m. Determine π2 . Compiled by: Parul Dawar, Inderpreet Kaur, Gunjeet Kaur