Download Conservation of charge

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Electric charge is always conserved in an
isolated system
– For example, charge is not created in the
process of rubbing two objects together
– The electrification is due to a transfer of
charge from one object to another
– Charge can only be separated
Conservation of Electric
Charges
• A glass rod is rubbed with
silk
• Electrons are transferred
from the glass to the silk
• Each electron adds a
negative charge to the silk
• An equal positive charge
is left on the rod
The electric charge, q, is said to be quantized
– q is the standard symbol used for charge as a
variable
– Electric charge exists as discrete packets
– q = Ne
• N is an integer
• e is the fundamental unit of charge
• |e| = 1.6 x 10-19 C
• Electric: q = -e
• Proton: q = +e
Electrical conductors are materials in which
some of the electrons are free electrons
– Free electrons are not bound to the atoms
– These electrons can move relatively freely through
the material
– Examples of good conductors include copper,
aluminum and silver
– When a good conductor is charged in a small region,
the charge readily distributes itself over the entire
surface of the material
Electrical insulators are materials in which all of
the electrons are bound to atoms
– These electrons can not move relatively freely
through the material
– Examples of good insulators include glass, rubber
and wood
– When a good insulator is charged in a small region,
the charge is unable to move to other regions of the
material
• The electrical properties of
semiconductors are somewhere between
those of insulators and conductors
• Examples of semiconductor materials
include silicon and germanium
Charging by induction
requires no
contact with the object
inducing the charge
Charge Rearrangement in
Insulators
• A process similar to
induction can take
place in insulators
• The charges within
the molecules of the
material are
rearranged
• The term point charge refers to a
particle of zero size that carries an electric
charge
– The electrical behavior of electrons and
protons is well described by modeling
them as point charges
q1q2
FK 2
r
Force between two point charges is
proportional to each charge inverse
proportional to the squared distance
between the charges
k is proportionality constant
(Coulomb constant)
Coulomb's Law, Notes
• Remember the charges need to be in
coulombs
e is the smallest unit of charge
e = 1.6 x 10-19 C
So 1 C needs 6.24 x 1018 electrons or
protons
• Typical charges can be in the µC range
• Remember that force is a vector quantity
q1q2 
F12  K 2 r
r
•In vector form,
• r is a unit vector
directed from q1 to q2
• The like charges
produce a repulsive
force between them
.The resultant force on any one charge
equals the vector sum of the forces
exerted by the other individual charges
that are present
– Remember to add the forces as vectors
• The resultant force on q1 is the vector
sum
of all the forces exerted on it by other
charges: F1 = F21 + F31 + F41
• The electric force is a field force
• Electric Charges are the source of the
electric field
• The electric field is defined as the
electric force on the test charge per unit
charge
• The test charge serves as a detector of
the field
Electric Charges
• There are two kinds of electric charges
– Called positive and negative
• Negative charges are the type possessed by
electrons
• Positive charges are the type possessed by
protons
• Charges of the same sign repel one
another and charges with opposite signs
attract one another
Electric Charges
•
There are two kinds of electric charges
–
Called positive and negative
•
Negative charges are the type possessed by
electrons
•
Positive charges are the type possessed by
protons
•
Charges of the same sign repel one
another
attract
and charges with opposite signs
one another
• Field lines are tangential to the field
• Field lines are directed from positive
charges toward negative charges
• The density of field lines is a measure for
the field strength
•The field lines radiate outward in all
directions
– In three dimensions, the
distribution is spherical
• The lines are directed
away from the source
charge
– A positive test charge would
be repelled away from the
positive source charge
• The field lines radiate inward in
all directions
• The lines are directed toward
the source
charge
A positive test charge would be
attracted
toward the negative source
charge
• The charges are equal
and opposite
• The number of field
lines leaving the positive
charge equals the
number of lines
terminating on the
negative charge
• The charges are equal and positive
• The same number of lines leave
each
charge since they areequal in
magnitude
• At a great distance,the field is
approximately equal to that of a
single charge of 2q
• The positive charge is twice
the magnitude of the negative
charge
• Two lines leave the positive
charge for each line that
terminates on the negative
charge
• At a great distance, the field
would be approximately the
same as that due to a single
charge of +q
• 2 Types of electric charges (pos. & neg.)
• Like charges repel one another
• Unlike charges attract one another
• Total amount of charge is conserved
• Charges move freely in conductors
• Charges cannot move in insulators
• Coulomb’s law describes force between
two point charges
• Electric field is created by charge
Chapter-1
Quantistion of charge
1. The charge of a body q = ne;
Where n is the number of charged particles and e = 1.6 x 1019C.
2. There are two types of charges, positive and negative. When a
glass rod is rubbed with silk, the glass rod becomes positive and
silk becomes negative. The glass rod and silk have equal and
opposite charges.
When an ebonite rod is rubbed with fur, the
charge on the ebonite rod is negative and that on fur positive.
Their charges are equal in magnitude.
3. Conservation of charge:
The charge can be transferred from
one body to another, but it can neither be charged
nor destroyed: total charge is conserved
4.Additivity of charges :
The total charge of a system of charges is
the algebraic sum of the charges.
5.The
basic properties of electric charges are
(i)quantization (ii) conservation and(iii)additivity.
6.Coulomb’s Law :
F=
 q1q2 
1
 
k 
 r2  4  0
 q1q2 
9  q1 q 2 
  2   9 10  2 
 r 
 r 
0 = 8.85 x 1012 C2 /Nm2; k = 9 x 109 Nm2/C2 (in free space)
7 Charge distributions
(a) Line charge density  = q/l (C/m);
(b) surface charge density  = q/A (C/m2);
(c) volume charge density p = q / v (C/m3)
8 Dipole moment p = 21 x q ; ‘21’ is the length of the
dipole. Its unit is mC. It is a vector whose direction is from
the negative charge to the positive charge.
8 Dipole moment
p = 21 x q ; ‘
21’ is the length of the dipole.
Its unit is mC. It is a vector whose direction
is from the negative charge to the positive charge.
9. Intensity of electric field.
(a) Due to a point charge q distant r from it E =
1
q
 2;
4  0 r
away from a positive charge and towards a negative charge.
(b) Due to an electric dipole:(i) At any point on its axis distant r from the center of the dipole.
2p
1
2 pr
1
E


 3 if r  l 
2
2
2
4  0 r  l
4  0 r


(ii) At any point on its equatorial line distant r from its center
 pr
 p
1
1
E


 3 if r  l 
3
/
2
4  0 r 2  l 2
4  0 r

10.

The dipole does not experience a net force
Torque on a dipole in a uniform electric field:
q pE
11.The electric flux,  =  E . d s (NC-1 m2)
If E is uniform over a surface,
 = E.A
If the surface of area A is
perpendicular to the uniform field lines,  = EA.
12. Gauss’ theorem states that the electric flux
through any closed surface in free space is 1 / 0 
times the total charge enclosed by the surface
=
1
 q
0
or
 E .ds 
1
 q
0
13.Field due to a line charge of linear charge
density

1
2

4  0
r
E=
14. Field due to an infinite sheet of uniform
surface-charge-density

20
E=
15.
Field due to a conducting spherical shell of radius. R and total
charge 1q are at a distance r from its center.
(i) E =
(ii) E =
1
q
 2 , if r  R
4  0
r
1
q
 , if r  R
4  0
R
(iii) E = 0 ; if r < R
The same is the case with a conducting sphere because, when the conducting
sphere is charged, the charge is uniformly distributed over its surface.
16.
Electric potential at a point is the work done to bring a unit
positive charge from infinity to the point. Unit: volt (V). It is a scalar
quantity.
17.
The p.d between any two points A and B is the work done to
bring a unit positive charge from A to B
VAB = VB  VA = 

B
A
E . dl .
the negative line integral of the electric field from A to B.
18 Potential at any point due a point charge,
V = (1/40) x
q
r
19 Even though the potential at a point is a scalar, the potential due
to a positive charge is positive and that due to a negative charge
is negative.
20 Electric field (E) at any point is the negative gradient of the
electric potential at that point E = - (dV/dr)
V = (1/40)
21 Electric potential due to a system of n charges.
V=(1/40)
i

n
il (qi / ri )
22. The electric potential inside a charged
conducting sphere (solid or hollow) is the same as
that on its surface.
23.Electric potential due to an electric dipole,
V=(1/40)x . p cos 
r2
On the axial line, = 0, and on the equatorial line  = 900.
• 24.
Equipotential surface is a surface where the
electric potential is same at every point on the surface.
• Ex : surface of a charged conductor.
• 25 Electric potential energy due to a system of two
q1 q 2
charges U=(1/40)
.
r
• 26.
Electric potential energy of a dipole placed
in an electric field, Up .=E .  PE cos 
•
When a dielectric medium (polar or non-polar) is
placed in an electric field, it acquires a net dipole
moment. This phenomenon is called dielectric
polarisation.
27.
For a conductor of charge Q and potential V,
Q  V or Q = C V, where C is a constant called the
capacitance (or capacity) of the conductor.
28.
A condenser (or capacitor) is an arrangement of conductor. If
there are two conductors at potential difference V and charge + Q and
– Q, C = Q / V.
29
Capacitance of a parallel plate condenser
• (a) with air between the plates is C = 0A/d; and with a dielectric
medium of dielectric constant K is C = K0A/d.
30.
When capacitors are in series 1/C ef f = 1/C1 + 1/C2 + . . . .;
and in parallel C ef f = C1 + C2 + C3 + …….
31.
Energy stored in the electric field between the plates of a
capacitor, i.e., potential energy, U=(1/2)CV2 = (1/2)QV = (1/2) Q2/C.