[2008EM/EVAL-QUIZ-02]

IMSc-IV Physics-IV : Electricity and Magnetism Jan-Apr 2008 MM : 20

[$\oslash$] Read the following passage and answer the questions given at the end. The numbers [1]-[10] in the text refer to the corresponding questions at the end.

The electrostatics and the magnetostatics are described by the four Maxwell's equations and correspond to a set of empirical laws discovered experimentally [1]. These equations divide into two sets of two decoupled equations each [2]. One of the Maxwell's equations incorporates the fact that the electrostatic forces are conservative [3]. Three important features of the electric field due to a point charge can be stated as [4,5] (a) the magnitude of the electric field at a point depends only on its distance from the point charge and not on the direction of the position vector (b) the inverse square law (c) the field is radial All the Maxwell's equations get coupled in when one considers a set of phenomena[6] discovered by a famous physicist [7]. However, Maxwell found an inconsistency [8] when he wrote the mathematical equations describing the electromagnetic phenomena known in his time. He used an important principle[9] to fix his equations and was led to introduce an extra term in one of the equations written for the static case. Maxwell then led to make an important prediction which unified electricity and magnetism with another branch of physics [10].

1. [{[1]}] Name the laws and corresponding mathematical forms.
2. [{[2]}] What is this division into two sets being referred to? Explain in one sentence.
3. [{[3]}] What is meant by a conservative force?
4. [{[4]}] Which set of the three properties (a), (b),(c) does not imply conservative force? Select one option from the following list  [(i)] all three & [(ii)] (a) and (b) & [(iii)] (a) and (c) & [(iv)] (b) and (c) 
5. [{[5]}] Name the famous law about the flux of the electric field. Do the properties (a) and (c) imply this law.
6. [{[6]}] What phenomenon couples all the Maxwell's equations?
7. [{[7]}] Who is this famous physicist who discovered this phenomenon?
8. [{[8]}] Which law for currents and magentic field start having problems?
9. [{[9]}] What important principle was used by Maxwell ? Give its mathematical form.
10. [{[10]}] Which branch of physics was unified with electricity and magnetism by Maxwell?