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Electromegnetism exercise

 

1.  Define gradient of a scalar point function. Give examples.

 

2. Define divergence of a vector point function with example. Give its physical significance.

 

3. Define curl of a vector point function with example. Give its physical significance.

 

4. Write a short note on (i) Equipotential surfaces, (ii) Displacement current.

 

5. What are the line, surface and volume integrals?

 

6. State and prove Stoke’s theorem.

 

7. State and prove Gauss’s divergence theorem.

 

8. State and prove Gauss theorem. Derive Coulomb’s law of electrostatics from Gauss’s theorem.

 

9. Obtain an expression of the field intensity at any point due to a line charge by Gauss’s  theorem.

 

10.Obtain an expression for the field intensity at any point due to infinite cylindrical charge by Gauss law.

 

11. State Ampere’s law in magnetostatics in integral form and from that deduce its differential form.

 

12.State Ampere’s circuital law.

 

13.Distinguish conduction current and displacement current.

 

14. What is the significance of displacement current?

 

15. Obtain the Maxwell’s equations of electromagnetism from fundamental laws of electricity

and magnetism

 

16. Write the Maxwell’s equations in integral and differential forms. Discuss their physical significance.

 

17. Derive an expression for the speed of light in free space.

18. Explain the concept of displacement current and show that it lead to the modification of  ampere’s law. Show that in free space the Maxwell’s equations lead to the relation

 

19. Define Poynting vector. Derive an expression for it and explain its physical significance for  c.m. waves in free space.