TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks

1. Time Varying Fields and Maxwell’s Equations 4.33
TWO MARKS QUESTION AND ANSWERS
1. State Faradays law?
The induced emf in any closed path or circuit is equal to the time rate of change of
magnetic flux linking the circuit
emf
d d
V N
dt dt
 

  
N denotes the number of turns
 is the flux through each turn
2. State Lenz law.
The induced current in the closed loop is in a direction such that the flux produced
by it tends to oppose the change in the original magnetic flux. This is Lenz law.
(or)
Lenz’s law states that the induced emf acts in such a way as to oppose the flux
producing it.
3. State Faradays law for a moving charge in a stationary (or) constant magnetic
field. (or) Define Motional EMF, (or) Flux cutting emf.
The Motional EMF produced by a moving conductor with a velocity, ‘v’in a constant
magnetic field ‘B’ is given by
 
emf
V v B dl
 




4. What is transformer EMF?
The emf induced in a closed path or closed circuit that is stationary while the
magnetic field B is varying with time is called as transformer emf.
emf
S
B
V E dl ds
t

    

 

5. Write the equation for point form of ohms law/Define conduction current
density.
J = E
Where  is the conductivity of the material in mhos per metre (  /m), J is the
conduction current density and E is the Electric field.

2. Electromagnetic Fields
4.34
6. Define Displacement current density.
Displacement current density JD
is given by
D
D E
J
t t

 
 
 
Displacement current density is due to time varying electric field. Its unit is A/m2
.
7. Distinguish between transformer emf and motional emf.
Transformer emf is induced in a stationary coil with time varying magnetic field.
Example : Transformer
Motional emf is induced when the coil rotates in a constant magnetic field.
Example : Generator
8. What is the significance of displacement current?
Displacement current is a result of time varying electric field. Without displacement
current, electromagnetic wave propagation is impossible. Example of displacement
current is the current through a capacitor when an alternating voltage source is
applied to its plates.
9. Write General Maxwell’s equations in point or differential form.
D
H J
t

  



 

(Ampere’s law)
B
E
t

  




(Faraday’s law)
V
D 
 

(Gauss law for Electric field)
0
B
 


Gauss law for Magnetic field)
10. Write the general form of Maxwell’s equations in integral form.
L S
D
H dl J ds
t
 

  
 

 
 


 

 (Ampere’s law)

3. Time Varying Fields and Maxwell’s Equations 4.35
L S
B
E dl ds
t

  

 



 (Gauss’s law)
V
V
S
D ds dv Q

   
 

 (Gauss law for Electric field)
0
S
B ds
 



 (Gauss law for Magnetic field)
11. Write the Maxwell’s equation for free space.
For free space  = 0, V
= 0
Integral Form : Differential Form :
S
D
H dl ds
t

 

 




D
H
t

 




S
B
E dl ds
t

  

 




B
E
t

  




0
S
D ds
 


 0
D
 

0
S
B ds
 



 0
B
 


12. Write the Maxwell’s equation for good conductors.
For good conductors, conductivity  is very high, charge density V
= 0.
Integral Form :
S
H dl J ds
  
 

 


S S
B
E dl ds
t

   

 




0
S
D ds
 




4. Electromagnetic Fields
4.36
0
S
B ds
 




Point Form or Differential Form :
H J
 

 

B
E
t

  




0
D
 

0
B
 


13. Write the Maxwell’s equations for harmonically varying fields.
Point form or Differential form :
 
H j E
 
  

 
E j H

  
 

V
D 
 

0
B
 


Integral Form :
 
S
H dl j E ds
 
   
 

 

S
E dl j H ds

   
 



V
V
S
D ds dv

 
 


0
S
B ds
 




14. Time varying field is not conservative. Prove it.
For convervative field E dl


 should be zero. But time varying electric field
produces a magnetic field and its value is given by Faraday’s law as,

5. Time Varying Fields and Maxwell’s Equations 4.37
.
B
E dl ds
t

 

 

So, Time varying field is not conservative.
15. Mention the parameters that limit the circuit approach for solving an electrical
problem.
Circuit theory is a two dimensional analysis. It cannot be used to calculate electric
and magnetic fields of a wave. Parameters of the medium like permittivity  and
permeability  are not involved in circuit approach. It cannot be used in high
frequency.
16. List the boundary conditions for time varying fields.
(i) The tangential component of Electric Field E is continuous at the boundary.
Et1
= Et2
and hence
1 1
2 2
t
t
D
D



(ii) Dn1
= Dn2
if the surface charge density is zero
Dn1
– Dn2
= S
if the surface charge density is non-zero and hence
1 2
2 1
n
n
E
E


 if
the surface charge density is zero.
(iii) Ht1
– Ht2
= JS
and hence
1 2
1 2
t t
S
B B
J
 
  where JS
is the surface current density.
.
(iv) Bn1
= Bn2
and hence
1 2
2 1
n
n
H
H



17. Write the Constitutive relations.
D E


 
B H


 

J E



 

6. Electromagnetic Fields
4.38
18. Define Wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at
other places at later times, the time delay being proportional to the space separation
from first location, then the group of phenomena constitute a wave.
19. What is a time harmonic field?
A tiume harmonic field is one that varies periodically or sinusoidally with time.
20. Define wave number.
K
u

 
 
K is called the wave number, u is the velocity of propagation
1
u


21. What is a Phasor?
A phasor is a complex number that contains amplitude and phase information of a
sinusoidal oscillation but is independent of t.
22. What is the wavelength range of visible light?
The wavelength range of visible light is from deep red at 720 nm to voilet at 380
nm or from 0.72 um to 0.32 um corresponding to a frequency range of from 4.2 
1014
Hz to 7.9  1014
Hz.
23. Why are frequencies below VLF range rarely used for wireless transmission?
Frequencies below VLF range are seldom used for wireless transmission because
huge antennas would be needed for efficient radiation of electromagnetic waves
and also because of the very low data rate at these frequencies.
24. Express E and B interms of potential functions V and A.
B A
 

 

A
E V
dt

  



25. Write the nonhomogenous wave equation for scalar potential V and for vector
potential A.
2
2
2
A
A J
t
 

   


7. Time Varying Fields and Maxwell’s Equations 4.39
2
2
2
v
V
V
t




   

26. What do you mean by a retarded potential?
 
1
,
4
V
V
R
t
u
V R t dV
R


 

 
 
  is called retarded scalar potential. It indicates that
the scalar potential at a distance R from the source at time t depends on the value of
charge density at an earlier time
R
t
u
 

 
 
. It takes time
R
u
for the effect of  to be
felt at a distance R. Hence V(R, t) is called retarted scalar potential.
Retarded vector potential is given by
 
1
,
4 V
R
J t
u
A R t dV
R

 

 
 
 
where
R
t t
u
   = Retarded time
27. Write the source free wave equations for E and H in free space (or) write
homogenous vector wave equations.
(i)
2
2
2
0
E
E
t


  

(or)
2
2
2 2
1
0
E
E
u t

  

(ii)
2
2
2
0
H
H
t


  

(or)
2
2
2 2
1
0
H
H
u t

  

Where
2 1
u

 , u is the velocity of propogation.
28. Write the homogenous vector Helmholtz’s equation for E in a simple, non
conducting, source free medium.
2
E
+ K2
E = 0
2
H
+ K2
H = 0
Where K
u


 