Download Module -2 For theory descriptive type questions please refer “A

Module -2
For theory descriptive type questions please refer “A textbook of Integrated Engineering Physics” by Dr. Amal Kr.
Chakrabarty
1
(i)
State
and
explain
Coulomb’s
law
in
electrostatics.
Express it mathematically
with meaning of each
symbol for two point
charges.
Does it depend on the
medium property? If yes,
then answer, how?
What
is
the
most
important requirement for
the validity of Coulomb’s
law?
Show that gravitational
force can be neglected
when compared with
Coulomb’s force.
(i)
(ii)
(iii)
(iv)
(v)
Refer Page 48
Refer Page 48
Refer Page 49
Refer Page 49
Refer Page 50
(i)
Define electric field E and
electric potential V at a
point and how they are
related.
(i)
(ii)
(iii)
Refer Page 49, 55, 66
Refer Page 65
Refer Page 66
(ii)
(iii)
Show that  E  0 .
In a place the electric
potential
is
same
everywhere. What is your
understanding about the
electric field intensity in
that place?
State and explain Gauss’
law in electrostatics. What
are its limitations?
Derive Coulomb’s law
from Gauss’ law.
Write
down
the
differential and integral
form of Gauss’s law.
Using Gauss’ law, find the
electric field intensity
outside, inside and on the
surface of (a) uniformly
(i)
(ii)
(iii)
Refer Page 61, 64
Refer Page 76
Refer Page 63
(ii)
(iii)
(iv)
(v)
2
3
(i)
(ii)
(iii)
4
a.
a. Refer Page (a) 75 and (b) 74
5
6
7
8
charged sphere (b) hollow
charged cylinder. Also
show
the
graphical
representation.
b.
The amount of net charge
enclose by a closed
surface is known, but
there is no idea about the
distribution of charges. In
this case, can Gauss’ law
be applied to determine
the electric field intensity
at any point of closed
surface? Explain.
a. Extend Gauss’ law to Poisson’s
equation. When does it reduce
to Laplace’s equation?
b. Write down Laplace’s
equation in Cartesian coordinate system. Two infinite
parallel plates at z=0 and z=a
are maintained at potentials
V0 and Va respectively. Obtain
the variation of potential and
field between the plates.
Write down Laplace’s equation in
Spherical co-ordinate system and find
the solution for spherical capacitor
considering the variation of potential
along radial direction.
Write down Laplace’s equation in
cylindrical co-ordinate system and find
the solution for cylindrical capacitor
considering the variation of potential
along radial direction.
(i)
Define
electronic
polarizability and Show
ε (ε −1)
(ii)
(iii)
that α = 0 r .
N
Show that D =ε0E + P.
What happens when a
non-polar molecule is
placed in an electric field?
b.
Within any point of the closed surface, it is
not possible to find the electric field but it is
possible to determine the field outside the
surface.
a. Refer Page 77
b. Refer Page 80
Refer Page 81
Refer Page 82
(i)
(ii)
(iii)
Refer Page 105 and 106
Refer Page 101
Refer Page 94
9
10
a. An amount of charge Q is
divided into two particles. Find
the charge on each particle so
that the effective force
between them will be
maximum.
b. Check whether the field E= 4yi
– 2xj + k is conservative.
c. If E= q/(4πε0r2) r then show
that E is solenoidal.
a. If the potential in the region of
space near the point (-2m, 4m,
6m) is V= 80x2 + 60y2 volt,
what are the three component
of electric field at that point?
b. If the electric field on a region
a. q, Q-q and F 
Kq(Q  q)
F

0
2
r
q
b. check if  E  0
c.
.E  0
a.
E  V
( 2,4,6)
b.   E.(75kˆ)
c.
1 1

2 3
is E  4iˆ  6 ˆj  7kˆ find the
electric flux through the
surface area of 75 square units
in XY plane.
c. S1 and S2 are two hollow
concentric spheres enclosing
charges Q and 2Q respectively.
What is the ratio of electric
flux through inner surface S1
and outer surface S2?
11
a. For positive x, y and z, let V =
40 xyz c/m3. Calculate the total
charge for the regions defined
by
(i) 0  x, y, z  2 .
b. The electric potential V(x) in a
region along the x-axis varies
with distance x (in meter)
according to the relation V(x) =
4x2. Calculate the force
experienced by 1 mC charge
placed at point x= 1m.
2
a.
2
2
    dxdydz
v
x 0 y 0 z 0
b.
E  V ; F  qE
12
In cylindrical coordinates (  ,  , z ) ,
.D  
electric flux density is given by
  ˆ 
 

 zˆ  .  z  cos 2  zˆ   
 ˆ
z 
   
D  z  cos 2  zˆ C/m2. Calculate the
  
,3  and the
 4 
charge density at  1,
total charge enclosed by the cylinder
of radius 1 meter with 2  z  2
meter.
13
a. A dielectric material contains 2
× 109 polar molecules/m3 each
of dipole moment 1.8 × 10–27
cm. Assuming that all of the
dipoles are aligned towards
electric field E = 105 V/m. Find
the
polarization,
electric
susceptibility and the relative
permittivity.
b. The dielectric constant of
helium at 0°C is 1.0000684. If
the gas contains 2.7x1025
atoms/m3, find the radius of
the electron cloud.
  
,3 
 4 
At  1,
And Q 
  dV 
1
2
2
  
 
 2 d  d dz
0 0 z 2
P
;r  K  1 
0 E
a.
P  n p;  
b.
K  1  4 na 3