This is the first set of questions presented here on electromagnetism and vector-analysis course for an engineering 1st year class. This is also useful for ‘hons’ and ‘pass’ Physics students. This was a course I delivered to engineering first years, around 9th November 2009. The slides were compiled; 25 Aug 2015. Next; Lectures and question-set on ‘electromagnetic waves’ and ‘Oscillations and Waves’. You can write me at g6pontiac@gmail.com or visit my website at http://mdashf.org

1. MANMOHAN DASH, PHYSICIST, TEACHER !
Physics for ‘Engineers and Physicists’
“A concise course of important results”
Complement-1
Question Pool >> ‘Vectors and Electromagnetism’
A collection of 24 short and long answer type
questions on the chapters we just finished >>
Lecture-1 and Lecture-2 !
25-08-2015

2. Recapitulation !
We discussed the ‘vectors and fields’ in the first
lecture and ‘laws of electromagnetism’ in the 2nd.
Lecture–1 Vector Calculus and Operations
Lecture–2 Electrodynamics
‘Here are a set of relevant questions. Have a look
at the lectures linked below, if you want to attempt
to solve the problem’
>> Lecture-1 << and >> Lecture-2 <<

3. Vector definitions, properties. Electromagnetic Fields
0)ˆ)()
3))





riv
r
V
rrViii
riirdVdVi


Q1. Prove the following with details. Q2. Prove that.
0)
0)


Aii
i



Q5. Define Gradient,
Divergence and Curl.
Q4. Define Solenoidal and
Irrotational field.
Q6. Define line, surface and volume integral of a vector field. Write the
flux of E (electric field) as a surface integral.
Q3. Define Electric Field E,
Electric Displacement vector D
and Electric Flux Phi.
EDE ,,

?

4. Vector Properties. Electromagnetic Fields.
Q7. Write the integral
form of gradient,
divergence and curl.
Q8. State Coulomb’s law of electrostatic
force mathematically and in words. State
Gauss Law in Electrostatics.
Q9. Use Gauss Law of Electrostatics
to derive the E (electric field) due to
a point charge at a distance r from it.
Q10. Write the Lorentz force F on
a charge q, moving at a velo-
city v in a magnetic field B.
Q11. Write the Biot-Savart
Law. Define flux of B.
Q12. Define magnetic intensity
H & magnetic flux Phi.
Q13. What are the cgs and SI unit of magnetic field B?
Q14. Write the integral and differential form of Gauss Law in
Electrostatics and Gauss Law in Magnetism >>
?


,
? BH ,

qv
FB B
,
,



5. Laws of Electromagnetic phenomena.
Q15. Write the integral form
of Maxwell’s electromagnetic
equations.
Q16. Derive the differential form of
Ampere’s Circuital Law from its
integral form.
Q17. Write the Ampere’s Circuital Law, Use Ampere’s circuital law to
derive magnetic field B due to a straight current carrying conductor.
Q18. Whats Maxwell’s displacement current Id? From the concept of Id in
a simple circuit with a capacitor of charge q & area A derive a general form
for Id. That is, derive;
Q19. Whats Faraday’s Law of E-M induction. Derive its differential form.
Q20. By using the following derive the equation
of continuity.
?
t
q
ISdjI
S


  ,

B

t
I E
d




0

6. Laws of Electromagnetic Phenomena
Q21. State modified Ampere’s Circuital Law. Its also known as Ampere-
Maxwell relation. Write its differential form.
Q22. Write the 4 Maxwell’s electromagnetic equations in differential form,
in terms of fields E, B, H, D with sources of charge and currents
?
DHBE

,,,

7. Long Answer Type Questions; Electromagnetic Phenomena
Q23. Use Stoke’s Theorem to convert integral form of
Ampere’s Circuital Law to its differential form. Derive
the equation of continuity. Explain its Physical
Significance.
?IldB
C
0

Ampere’s Circuital
Law in integral form
0



t
j

Equation of
Continuity
?

8. Long Answer Type Questions; Vector Calculus
Q24. Prove the Green’s Theorem. Hint; Use Gauss
Divergence Theorem and identities from vector calculus.
?
dvfggfsdfggf
V
  )()( 22
Green’s Theorem

9. Thank you
This is the first set of question presented here on
electromagnetism course for an engineering 1st year class.
This is also useful for ‘hons’ and ‘pass’ Physics students.
This was a course I delivered to engineering first years, around
9th November 2009. The slides were compiled; 25 Aug
2015.
Next; Lectures and question-set on ‘electromagnetic waves’
and ‘Oscillations and Waves’. You can write me at
g6pontiac@gmail.com or visit my website at
http://mdashf.org