Long ANswer Type Questions from Electrostatics

  1. Obtain an expression for the electric field intensity due to a uniformly charged ring of radius r at a point on the axis of the ring.
  2. Express Coulomb’s law in vector for.
  3. Derive an expression for the electric field due to an electric dipole at a point on (a) the axial line (b) the equatorial line.
  4. Derive an expression for the torque acting on an electric dipole placed in a uniform electric field.
  5. Show that the work done in rotating an electric dipole of dipole moment p in a uniform electric field E by an angle ? from the equilibrium postition W = PE(1-cos ?)
  6. Derive Coulomb’s law from Gauss’ law.
  7. Use Gauss theorem to derive an expression for the electric field at a point due to an infinite plane sheet of charge of uniform charge density ?
  8. Use Gauss theorem to derive an expression for the electric field at a point due to a thin infinitely long straight line  of charge of uniform charge density ?
  9. Derive an expression for the electric field at a point due to uniformly charged spherical shell using Gauss’ law.
  10. Derive an expression for the capacitance of a parallel plate capacitor.
  11. Find the equivalent capacitance of three capacitors of capacitances C1, C2 and C3 connected in (1) series (2) parallel
  12. Derive an expression for the electric potential due to a point charge q at a distance r from it.
  13. Giving a labeled diagram explain the principle and working of a Van de Graaff generator.
  14. A dielectric slab of thickness t introduced between the plates of a parallel plate capacitor separated by a distance d. (t < d). DEerive an expression for the capacitance of the capacitor.