1. Electric forces and electric fields

2. 1. Proprieties of electric charges
Electric charge can be + or –
Like charges repel one another; and unlike charges attract one another
Electric charge is always conserved

3. The object become charged because – charge is transferred from one object to another
An object may have charge of ±e, ±2e, ±3e
e = x10-19C
SI unit: C (Coulomb)
2 Insulators and conductors
In conductors, electric charges move freely in response to an electric force. All other materials are called insulators (give an ex. of each)
Semiconductors are between conductors and insulators.

4. An object connected to a conducting wire buried in the Earth is said to be grounded.
Induction – charging of a conductor
Charging an object by induction requires no contact with the object inducing the charge.

5. 3. Coulomb’s Law
An electric force has the following properties:
It is directing along a line joining the two particles and is inversely proportional to the square of the separation distance r, between them
It is proportional to the product of the magnitudes of the charges, |q1|and |q2|, of the 2 particles
It is attractive if the charges are of the opposite sign, and repulsive if the charges have the same sign

6. The magnitude of the electric force:
F=ke (|q1||q2|/r2)
ke – Coulomb constant
ke = x109N m2/C2

7. 4. Electric Field
The electric field E produced by a charge Q at the location of a small “test” charge qo is defined as the electric force F exerted by Q and qo divided by the charge qo .
E=F/qo
E=ke (|q|/r2)
Si unit : N/C

8. Pb. Strategies:
1. Draw a diagram of the charges
2. Identify the charge of interest
3. Convert all units in SI
4. Apply Coulomb’s Law
5. Sum all the x- components of the resulting electric force
6. Sum all the y-components of the resulting electric force
7. Use Pythagorean theorem to find the magnitude and the direction of the force

9. 5. Electric field lines
1. The electric field E is tangent to the electric field lines at each point
2. The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region

10. Rules for drawing electric field lines:
-The lines for a group of point charges must begin on + charge and end on – charge
- The number of lines drawn leaving a + charge or ending a – charge is proportional to the magnitude of the charge
- No two field lines can cross each other

11. 6. Conductors in electrostatic equilibrium
When no net motion of charge occurs within a conductor, the conductor is in electrostatic equilibrium
Proprieties of an isolated conductor:
1. the electric field is zero inside of the material
2. any excess charge on an isolated conductor resides entirely on its surface
3. the electric field just outside a charge conductor is perpendicular to the conductor’s surface
4. On an irregularly shaped conductor , the charge accumulates at sharp points, where the radius of curvature of the surface is smallest

12. 7.electric flux and Gauss’s Law
The electric flux ( the number of the field lines) is proportional to the product of the electric field and surface of the area
ΦE =EA
ΦE =EA cosθ

13. For a close surface, the flux line passing into the interior of the volume are negative, and those passing out of the interior of the volume are positive

14. Gauss’s Law:
E= ke q|/r2
A= 4πr2
ΦE =EA=4π ke q
ΦE =q/ εo
Permittivity of free space:
εo=1/(4π ke )=8.85x10-12C2/Nm2
The electric flux through
any closed surface is equal
to the net charge inside the
surface divided by the
permittivity

15. 8. Potential difference and electrical potential
Work and potential energy:
Potential energy is a scalar quantity with change to the negative of the work done by the conservative force
ΔPE=Pef-Pei =- Wf
Coulomb force is conservative
If imagine a small + charge placed in a uniform electric field E. As the charge moves from A to B, the work done on the charge by the electric field:
W=FxΔx =q Ex (xf-xi)

17. Work –energy theorem
W=q Ex Δx =ΔKE
But the work done by a conservative force can be reinterpreted as the negative of the charge in a potential energy associated with that force
ΔPE of a system consisting on an object of charge q through a displacement Δx in a constant electric field E is given by:
ΔPE =-WAB= -q Ex Δx
SI unit J (Joule)

19. Δ KE + ΔPE el = ΔKE +(0-ΙqΙ E d) =0
Similarly , KE equal in magnitude to the loss of gravitational potential energy:
ΔKE +ΔPEg =ΔKE +(0 –mgd) =0
ΔKE=mgd

20. Electric Potential
F = qE
The electric potential difference between points A and B is the charge in electric potential energy as a charge q moves from A to B, divided by the charge q: ΔV =VA-VB = ΔPE/q
SI unit J/C or V (Joule/Coulomb or Volt)
Electric potential is a scalar quantity

22. Electric potential created by a point charge: V=ke q/r
9.Electric potential and potential energy due to point charges
The electric field of a point charge extends throughout space, so its electrical potential also
Electric potential created by a point charge: V=ke q/r
The electric potential of two or more charges is obtained by applying the superposition principle: the total electric potential at some point P due to several point charges is the algebraic sum of the V due to the individual charges

25. The electric potential at all points on a charged conductor
10.Potentials and charged conductors
The electric potential at all points on a charged conductor
W= -ΔPE =-q( VB-VA)
No net work is required to move a charge between two points that are at the same electric potential
All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential

26. The electric potential is a constant everywhere on the surface of a charged conductor
The electric potential is constant everywhere inside a conductor and equal to the same value at the surface
The electron volt is defined as KE that an electron gains when accelerated through a potential difference of 1V
1eV =1.6x C V =1.6x10-19 J

27. Equipotential surface is a surface on which all points are at the same potential
The electric field at every point of an equipotential surface is perpendicular to the surface.

29. 11.Capacitance
A capacitor- is a device used in variety of electric circuits
The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between conductors (plates)
C=Q/ΔV
SI unit F (Farad)=C/V

30. 12.The parallel-plate capacitor
C=q/ΔV
ΔV=Ed; E=σ/ε0 ; q=σA
C=σA/Ed=σA/(σε0)d
C= ε0A/d

31. Symbols for circuit elements and circuits

33. 13 Combinations of capacitors Capacitor in Parallel

34. Capacitors in parallel both have the same potential difference across them
Q=Q1+Q2
Q1= C1ΔV
Q2 = C2ΔV
Q= Ceq ΔV
CeqΔV=C1ΔV+C2ΔV
Ceq=C1+C2 (parallel combination)

35. Capacitors in series

36. Electrical Energy and Capacitance
For a series combination of capacitors, the magnitude of the charge must be the same on all the plates
ΔV=Q/Ceq
ΔV1=Q/C1; ΔV2=Q/C2; ΔV=ΔV1+ΔV2
Q/C= Q/C1+Q/C2
1/C= 1/C1+1/C2 (series combination)
Electrical Energy and Capacitance

37. 14. Capacitors with dielectrics

38. A Dielectric- is an insulating material (rubber, plastic, waxed paper)
If a dielectric is inserted between the plates, the voltage across the plates is reduced by a factor k (dielectric constant) to the value:
ΔV =ΔV0/k
C=k C0
C=kε0 A/d
The maximum electric field is called dielectric strength