Transcript Electric forces and electric fields

Electric forces and
electric fields
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
The object become charged because – charge
is transferred from one object to another
 An object may have charge of ±e, ±2e, ±3e
 e = 1.60219x10-19C
 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.
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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.
3. Coulomb’s law
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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
The magnitude of the electric force:
 F=ke (|q1||q2|/r2)
 ke – Coulomb constant
ke = 8.9875x109N m2/C2
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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 .
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E=F/qo
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E=ke (|q|/r2)
 Si unit : N/C
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
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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
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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
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
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
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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
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
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:
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)
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Δ KE + ΔPE el = ΔKE +(0-ΙqΙ E d) =0
 ΔKE = ΙqΙ E d
 Similarly , KE equal in magnitude to the
loss of gravitational potential energy:
 ΔKE +ΔPEg =ΔKE +(0 –mgd) =0
 ΔKE=mgd
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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
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
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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
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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 10-19 C V =1.6x10-19 J
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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.
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
12.The parallel-plate capacitor
C=q/ΔV
ΔV=Ed; E=σ/ε0 ;
q=σA
C=σA/Ed=σA/(σε0)d
C= ε0A/d
Symbols for circuit elements and circuits
13 Combinations of capacitors
Capacitor in Parallel
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)
Capacitors in series
For a series combination of capacitors, the
magnitude of the charge must be the same
on all the plates
ΔV=Q/C
eq
Electrical
Energy and
ΔV1=Q/C1; ΔV2=Q/C2; ΔV=ΔV1+ΔV2
Capacitance
Q/C= Q/C1+Q/C2
1/C= 1/C1+1/C2 (series combination)
14. Capacitors with dielectrics
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
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