Transcript Chpt 6 - Electrostatic

SUBTOPIC
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Charge units
Electric field
Electric force & Coulomb’s Law
Capacitance and unit
Parallel plate capacitor
Dielectric constant and it’s function
Introduction
Electrostatics (also known as static electricity) is the branch of
physics that deals with the phenomena arising from what seem
to be stationary electric charges. This includes phenomena as:
(i) simple as the attraction of plastic wrap to your hand after you
remove it from a package to apparently spontaneous explosion of
grain silos,
(ii) to damage of electronic components during manufacturing,
(iii) to the operation of photocopiers.
Electrostatics involves the buildup of charge on the surface of
objects due to contact with other surfaces.
Introduction
Electric Charge
Electric charge is a fundamental property of matter; electric charges may be
positive or negative.
The atom consists of a small positive nucleus is surrounded by a negative
electron cloud.
Electric Charge
Is an intrinsic characteristic of the fundamental particles making up those
objects; that is, it is a characteristic that automatically accompanies those
particles wherever they exist.
Charges with the same electrical sign repel each other; and charges with
opposite electrical signs attract each other.
Electric Charge - Lightning
Electric Charge
SI unit of charge: the coulomb, C. All charges are integer multiples of the
charge on the electron:
n = 1, 2, 3,..
Conservation of charge:
The net charge of an isolated system remains constant.
Net charge of the universe is constant !!!
Electrostatic Charging
Conductors transmit charges readily.
Semiconductors are intermediate; their
conductivity can depend on impurities and
can be manipulated by external voltages.
Insulators do not transmit charge at all.
Electrostatic Charging
An electroscope may be used to determine if an object is electrically charged.
Electrostatic Charging: FRICTION
Charging by friction: This is the process
by which you get “charged up” walking
across the carpet in the winter.
It is also the process that creates “static
cling” in your laundry, and makes it
possible for you to rub a balloon on your
hair and then stick the balloon to the
wall.
Electrostatic Charging: CONDUCTION
An electroscope can be given a net charge by conduction – when it is
touched with a charged object, the excess charges flow freely onto the
electroscope.
Electrostatic Charging: INDUCTION
An electroscope may also be charged by induction, if there is a way of
grounding it while charge is being induced.
Electrostatic Charging: POLARIZATION
Charge may also be moved within an object – without changing its net charge
– through a process called polarization. (charge separation by polarization)
Electric Force
For the two point of charges, depend directly to the product of the
magnitude of the charges and inversely on the square root of the
distance between them:
q1 q 2
Fe  2
r
kq1q2
 Fe  2
r
Called Coulomb’s Law
k
1
40
 8.988 109 Nm2 / C 2  9.00 109 Nm2 / C 2
 0  8.85 10 12 C 2 / Nm2
kq1q2
F12  2
r
q1
q2
r
F21 
kq1q2
r2
Electric Force
If there are multiple point charges, the force vectors must be added to get
the net force.
EXAMPLE 1
q1 = -1nC
F12
F21
q2 = +2nC
0.3m
(a) Two point charges of -1.0nC and +2.0nC are separated by a distance of 0.3m, what
is the electric force on each particle?
y
(0, +0.3m)
q1 = +2.5nC
r31


r32
(0, -0.3m)
q3 = +3.0nC
x
(0, 0.4m)
q2 = +2.5nC
(b) What is the net electric force on q3 ?
Solution:
(a)
kq1q2
F12  F21  2
r
(9 109 Nm2 /C 2 )(110 9 C)(2 10-9 C)

(0.3m) 2
 0.2 10-6 N  0.2N
y
q1 = +2.5nC
(b)
F32


F31
q2 = +2.5nC
Fnet = F3
x
Solution:
(b)
r31 = r32 = 0.5m
kq2 q3 (9 109 Nm2 /C 2 )( 2.5 10 9 C)(3.0 10-9 C)
F32  2 
r
(0.5m) 2
 0.27 N
Taking into account the direction of F31 and F32 is symmetry – then y – components
cancel. Thus, F3 (the net force on q3) acts along the positive x-axis and has magnitude of
F3  F31  F32  2F31
 0.3m 
o
  37
 0.4m 
  tan 1 
F3  2 F31  2 F32 cos   2(0.27 N)cos37 o  0.43N
EXAMPLE 2
(a) What is the magnitude of the repulsive electrostatic force between two
protons in a nucleus? Taking the distance from center to center of these
protons to be 3 x 10-15m.
b) If the protons were released from rest, how would the magnitude of their
initial acceleration compare with that of the acceleration due to gravity on
Earth’s surface, g ?
Solution:
Given: r = 3 x 10-15m; q1=q2 = +1.6 x 10-19C ; mp = 1.67 x 10-27kg
(a) Using Coulomb’s Law;
kq1q2 (9 109 Nm2 /C 2 )(1.6 10-19 C)2
Fe  2 
 25.6N
-15
2
r
(3 10 m)
(b)
Fe
25.6N
28
2
a


1
.
53

10
m/s
m p 1.67 10-27 kg
a 1.53 1028 m/s 2
27


1
.
56

10
g
9.8m/s 2
Electric Field
The electric field at any location is
defined as follows:
E
Fon q 
q
(kqq / r 2 ) kq

 2
q
r
SI Unit: N/C
The direction of the field E is the direction the force would be on a positive
charge.
Electric Field
Charges create electric fields, and these fields in turn exert electric forces on
other charges.
Electric field of a point charge:
EXAMPLE 3
1. Two point charges are placed on the x-axis as shown in Fig. below. Find all
locations on the axis where the E = 0.
q1 = +1.5μC
q1 = +6μC
x
0.0
0.6
Solution
E1  E2
or
kq1
kq2

x 2 (d  x) 2
Where, d is the distance of q2, rearranging this expression,
1 (q2 / q1 )

2
x (d  x) 2
With q2/q1 = 4, taking square root of both sides:
1
q2 / q1
1
2

 
2
2
x
(d  x)
x dx
Thus;
x
d 0.6m

 0.2m
3
3
EXERCISE 1
y
q1
q3
d
d
30o
30o
d
30o
x
q2
1. Fig. above shows three particles with charge q1 = +2Q, q2 = -2Q, and q3 = -4Q, each
a distance d from the origin. What net electric field E is produced at the origin?
y
-8μC
s
s
+2μC
P
s
x
+12μC
2. Find the electric field at point P due to the charges shown where s = 50cm.
Electric Field
Electric field lines due to very large parallel plates:
Q – magnitude of total charge on one of the plates; A – area of one plate.
Electric Field
Electric field lines due to like charges: (a) equal charges; (b) unequal charges.
Electric Field
Conductors and Electric Fields
Electric charges are free to move within a conductor; therefore, there
cannot be a static field within the conductor:
The electric field is zero inside a charged conductor.
Excess charges on a conductor will repel each other, and will wind up being
as far apart as possible.
Any excess charge on an isolated conductor resides entirely on the surface of
the conductor.
Conductors and Electric Fields
There cannot be any component of the electric field parallel to the
surface of a conductor; otherwise charges would move.
The electric field at the surface of a charged conductor is perpendicular
to the surface.
Conductors and Electric Fields
The force from neighboring charges is less when the curvature of the surface
is large:
Excess charge tends to accumulate at sharp points, or locations of highest
curvature, on charged conductors. As a result, the electric field is greatest at
such locations.
PART 2
Electric Potential, Energy & Capacitance
Electric Potential Energy
• To move a charge from one point to another point in E, a work need to be
done
• Work done by external force to move a +ve charge (+q) from A to B in E
=F/q by a charge +Q state as:
b
b
a
a
W   F ' dr   F ' cos dr
+Q
UB
dr = charge displacement
θ = angle between F’ and dr
F’ =F by E, but in different direction
+q
E=F/q
UA
• When charge moves from UA to UB, energy changes  U  U A  U B  W
• In general, electric potential energy given by
U 
 F .dr  q  E.dr
kQq
U 
r
Electric Potential
• Definition: Electric potential energy per unit charge
U
kQ
V 
  E.dr 
q
r
• Unit: Volt or JC-1
• For a number of Q1, Q2 and Q3 at distance r1,r2 and r3 from
point P
+Q1
r1
P
r2
+Q2
r3
+Q3
Qi
Q1 Q2 Q3
V  k(


)  k
r1
r2
r3
ri
Electric Potential Energy
& Electric Potential Difference
Electric Potential Energy
It takes work to move a charge against an electric field. Just as with gravity,
this work increases the potential energy of the charge.
Gravity !!!
Electric Potential Energy
& Electric Potential Difference
Just as with the electric field, it is convenient to define a quantity that is the
electric potential energy per unit charge. This is called the electric potential.
Electric potential difference
SI unit of electric potential: Joule/Coulomb or the volt, V.
Electric Potential Energy
& Electric Potential Difference
The potential difference ∆V between parallel plates can be calculated
relatively easily:
d – separation between two parallel plates.
For a pair of oppositely charged parallel plates, the positively charged
plate is at a higher electric potential than the negatively charged one by
an amount ΔV.
Electric Potential Energy
& Electric Potential Difference
As with potential energy, only changes in
the electric potential can be defined. The
choice of V = 0 is arbitrary.
∆V is independent of reference point !!!
Electric Potential Energy
& Electric Potential Difference
Potential differences are defined in terms of positive charges, as is the
electric field. Therefore, we must account for the difference between
positive and negative charges.
Positive charges, when released, accelerate toward regions of lower electric
potential.
Negative charges, when released, accelerate toward regions of higher
electric potential.
EXAMPLE 4
Imagine moving a proton from negative plate to the positive plate of the
parallel-plate arrangement. The plates are 1.5cm apart, and the field is uniform
with a magnitude of 1500 N/C.
(a) What is the change in the proton’s electric potential energy?
(b) What is the electric potential difference (voltage) between the plates?
(c) If the proton is released from rest at the positive plate, what is the speed will it
have just before it hits the negative plate?
Solution:
Given: E = 1500 N/C ; qp = +1.6 x 10-19C ; mp = 1.67 x 10-27kg ; d = 1.5 x 10-2m
(a)
(b)
(c)
U e  q p Ed  (1.6 10-19 C)(1500N/C)(1.5 102 m)  3.6 10-18 J
U e  3.6 10 18 J
V 

 22.5V
19
q p  1.6 10 C
Total energy of proton is constant
K  U  0
K  K  K 0  K  K  K  U e Initial, K0 = 0
1
m p v 2  U e
2
v
2(U e )
 6.57 10 4 m/s
mp
∆U is negative – when its return
to negative plate
Electric Potential Energy
& Electric Potential Difference
Electric potential difference of a
point charge:
Electric Potential Energy
& Electric Potential Difference
Whether the electric potential increases or decreases when towards or away
from a point charge depends on the sign of the charge.
Electric potential increases when moving nearer to positive charges or
farther from negative charges.
Electric potential decreases when moving farther from positive charges or
nearer to negative charges.
Electric Potential Energy
& Electric Potential Difference
The electric potential energy of a system of two charges is the change in
electric potential multiplied by the charge.
kq1q2
U 12 
r12
Mutual electric potential energy
(two charges)
Electric Potential Energy
& Electric Potential Difference
The additional potential energy due to a third
charge is the sum of its potential energies
relative to the first two. Further charges extend
the sum.
Capacitance
A pair of parallel plates will store electric energy if charged oppositely; this
arrangement is called a capacitor.
Capacitance
The charge is related to the potential difference; the ratio is called the
capacitance.
SI unit of capacitance: the farad, F.
For a parallel-plate capacitor,
or
C
0 A
d
Michael Faraday
(1791 – 1867)
British physicist
The quantity inside the parentheses is called the permittivity of free
space, ε0.
Capacitance
The energy stored in a capacitor is the energy required to charge it:
EXAMPLE 5
A parallel plate capacitor with a plate of 0.25 m2 and a plate separation of 6.00 mm is
connected with 12 V source. Find:
(a) Charge on the capacitor
(b) Energy stored in the capacitor
(c) Potential difference across the capacitor is reduce to half, explain what will happen
to charge on the capacitor and its stored energy
Solution:
(a)
C
 oA
d
(8.854  10-12 )(0.25m 2 )

0.006m
 36.9  10 9 F
(b)
(c)
1
CV 2
2
1
 (36.9 10-9 F)(12 V) 2
2
 2.66 10 6 J
UC 
Since Q = CV, it half.
Since UC = ½ CV 2, it doubles.
Dielectrics
A dielectric, or electrical insulator, is a substance that is highly resistant to
the flow of an electric current.
Although a vacuum is also an excellent dielectric, the following discussion
applies primarily to physical substances.
The use of a dielectric in a capacitor presents several advantages. The
simplest of these is that the conducting plates can be placed very close to
one another without risk of contact. Also, if subjected to a very high electric
field, any substance will ionize and become a conductor.
Dielectrics
“Dielectric” is another word for insulator. A dielectric inside a capacitor
increases the capacitor’s energy storage by an amount characterized by the
dielectric constant, .
Dielectrics
A dielectric in an electric field becomes polarized; this allows it to sustain a
larger electric field for the same potential difference.
The net effect: E and V <<,
Stored charge remains the same
- Capacitance increase.
Dielectrics
The dielectric creates a ‘reverse’ electric field – that partially cancels the field
between the plates. The  of the material is define as ratio of voltage with the
material in place (V) to the vacuum voltage (V0), and because V proportional to E, thus
V0 E0
 
V E
Only when the capacitor charge is
constant
 is dimensionless and > 1.000
The capacitance of a capacitor containing a dielectric is increased. The
definition for capacitance is
or
Dielectrics
Inserting a dielectric into a
capacitor while either the voltage
or the charge is held constant has
the same effect – the ratio of
charge to voltage increases.
Voltage drops
Stored energy decrease
Charge on a plates increase
More energy stored in capacitor