1. Express Coulombs force (name each component in the relation).

K= Colomb constant

Q1Q2 = charges

R= distance between charges

2. Define electric field intensity (name each component in the relation). -The force per unit charge is equal describes a vector field called the electric field intensity:

3 What are field streamlines and how are they useful? -The dreamlines (flux lines) are direction lines that are tangent to the force field vector. They are useful

because they show the direction of a field. The closer the streamlines are, the stronger the field (and

other advantages of sketching streamlines)

4. Define electric flux density.

Electric flux density is the flux density distributed over a surface divided by the are of that surface:

5. Write Gausss law for electric field in the global form.

Generalization of Faradays experiment: the electric flux passing through any closed surface is equal to

the total charge enclosed by that surface. The Gauss contribution was in providing the mathematical

form of the law:

[N]2

21

R

QQkF

04

1

k

[F/m]10854.81094

1 1290

[V/m]or[(Nm/C)/m]4 2120

1t

t

t

R

Q

Q1a

FE

][C/m4

2

2 rr

Q

AaD

0 ED

SDS SS SSD cosD crossingflux normS,

SD dd S

The total flux passing through a closed surface is:

6. The point form of Gausss law for electric field (Maxwells first equation of electrostatics).

7. Express the divergence of a vector in Cartesian coordinates.

8. The divergence theorem (Gauss theorem).

9. Define electric potential difference. Potential difference is the work done by an external source in moving a unit positive charge from one

point to another in an electric field.

10. Express the gradient of a scalar in Cartesian coordinates.

11. Express electric field intensity vector using electric scalar vector. E=-grad V= dv/dn*Qn

12. What is a conservative field and how is the circulation in an electric conservative field? As potential difference between two points in a static field does not depend on path results that:

This relation is true only in static electric fields (not if E variable or in presence of variable magnetic

field Faraday). Such fields are called conservative fields (energy is conserved)

13. What is the expression of electric energy density depending on electric intensity and electric flux

density?

Qdd S

SD

v

dS

v

A

A0

limdivvDdiv

z

A

y

A

x

A zyx

Adiv

vol

S dvd DSD

zyxzyxaaa

zyxz

T

y

T

x

TT aaa

0LE d

]J/m[2

1 3DE

dv

dWw EE

14. Define convection current density (name each component in the relation).

15. Ohm law in point form (dependence between current density and electric field intensity) - (name each component in the relation).

16. Define dipole moment and polarization in a dielectric material. Either type of dipole can be described depending on dipole moment p:

where Q is positive charge of one of the two bound charges, d vector from to + charge.

By definition polarization P is the dipole moment per unit volume:

17. Mention couple differences between a conductor and a dielectric. No free charges, thus no conduction.

Electrons bounded (bound charges) by atomic and molecular forces can only shift position slightly, in

response to external fields.

Bound charges create electrostatic field as any other electric charge.

Dielectrics have capacity to store electric energy.

18. Write the relations of the conduction current density and convection current density. Explain the difference. 19. Relation between electric flux density and electric intensity field in a dielectric (name each com-ponent in the relation).

D- electric flux density

D= 0E E- electric field intensity

vJ vvvdS

dIJ

L

VE

S

IJ AB

S

LI

S

LIU

RIU

dp Q

][limP2

10

C/m1

n

i

iv

pv

20. Boundary conditions in a dielectric (relations between tangent and normal component of the electric field intensity and of the electric flux density).

21. Expression of the capacitance of a two-plate conductor capacitor and the energy stored in such ca-pacitor.

22. Write the Poisson equation for the electrostatic field and Laplace operator in Cartesian coordinates.

23. What can produce a steady magnetic field? Source of steady magnetic field: permanent magnet, direct current (DC), electric field changing linearly

with time.

24. What is the Biot-Savart law expressing?

25. Write Amperes circuital law in integral form and point (local) form.

26. The dependence between magnetic flux density (density) and magnetic field intensity. Explain each component and name the measuring units.

In free space only B=0H

-0 - is magnetic permeability in free space; -B- magnetic flux density [T] -H- magnetic fields intensity;[A/m] 27. Gauss theorem for magnetic flux in global form.

1

2

2

1

cos

cos

D

D

2

1

2

1

22

11

2tan

1tan

tan

tan

sin

sin

D

D

D

D

2

2

2

1

2

1

2

1

C

QQUCUWE

v D

ED VE

vz

V

y

V

x

VV

2

2

2

2

2

2

24 R

Id

RaLH

IdLH

]T[0HB 0 B

28. Gauss theorem for magnetic flux in local form.

29. Express magnetic flux density using the vector magnetic potential. A- vector magnetic potential 30. Why is magnetic force exerting upon of a charge particle not changing kinetic energy of the particle? Force F=(v x B) does not do any work on the particle as it is perpendicular to the velocity.

Hence magnetic force does not cause any change in kinetic energy or speed of the particle.

31. Lorentz force equation (name each component in the relation). F-force

F=force [N]

E= electric field[V/m]

B= magnetic field [Tesla]

Q= electric charge [C]

v=velocity[m/s]

32. Ampere electro-dynamic forces explain when do they appear. Forces exerted between two filamentary straight parallel forces (Ampere) respect action-reaction

principle; the filaments are repelling each other if currents passing them are opposite direction; forces

are proportional with product between currents and inverse with distance between them.

33. What properties have magnetic materials give some examples. Six different types of material: diamagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic and

superparamagnetic

In ferromagnetic materials atoms have large dipole moments.

The atoms line up with dipole moment oriented in same way they form regions.

After applying a magnetic field regions do not all return back to initial random orientation

remnant magnetic field.

34. Define and draw a magnetization curve.

A graph, table, or formula that shows the dependence of the magnetization J or magnetic induction B on

the magnetic-field intensity H. If the function J(H) is known, then the induction curve B(H) can be

constructed for the same substance, since the simultaneous values of B, J, and H that refer to the same

volume element of the substance are related by the equation B = H + 4J (in the centimeter-gram-

second system of units) or B = 0 (H + J) (in SI units, where 0 is the magnetic constant).

0

SB d

BA

)( BvEF Q

35. Explain briefly magnetic saturation and hysteresis.

Ferromagnetic materials like iron that show saturation are composed of microscopic regions called magnetic domains that act like tiny permanent magnets. Before an external magnetic field is applied to the material, the domains are oriented in random directions. Their tiny magnetic fields point in random directions and cancel each other out, so the material has no overall net magnetic field. When an exter-nal magnetizing field H is applied to the material, it penetrates the material and aligns the domains, causing their tiny magnetic fields to turn and align parallel to the external field, adding together to cre-ate a large magnetic field which extends out from the material. This is called magnetization. The strong-er the external magnetic field, the more the domains align. Saturation occurs when practically all the domains are lined up, so further increases in applied field can't cause further alignment of the domains.

Hysteresis is well known in ferromagnetic materials. When an external magnetic field is applied to a ferromagnet, the atomic dipoles align themselves with the external field. Even when the external field is removed, part of the alignment will be retained: the material has become magnetized. For example, a piece of iron that is brought into a magnetic field retains some magnetization, even after the external magnetic field is removed. Once magnetized, the iron will stay magnetized indefinitely. To demagnetize the iron, it would be necessary to apply a magnetic field in the opposite direction. This is the effect that provides the element of memory in a hard disk drive.

36. Define inductance (explain each component in the relation). Inductance is the property of a cirtuit whereby there is an e.m.f. induced into the circuit by the change

of flux linkages produced by a current change

37. Write the expression of the magnetic energy.

38. Faradays law in integral form (both components of the emf).

39. Write Fradays law in differential form (the fourth Maxwells equation) (explain each component in the relation).

volvolvol

m dvdvdvW

2

2

2

1

2

1

2

1 BHHB

SBLE ddt

ddemf

dt

dNemf

t

BE

E-intensity field B=magnetic field nabla= the divergence of a vector 40. Shortly describe what were Faradays experiments to prove production of electric field (emf) by magnetic field. The EMF generated by Faraday's law of induction due to relative movement of a circuit and a magnetic

field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative

to a conductor, or vice versa, an electromotive force is created. If the wire is connected through an

electrical load, current will flow, and thus electrical energy is generated, converting the mechanical

energy of motion to electrical energy.