SUBTOPIC Charge units Electric field Electric force & Coulomb’s Law Capacitance and unit Parallel...

SUBTOPIC• Charge units• Electric field• Electric force & Coulomb’s Law• Capacitance and unit• Parallel plate capacitor• Dielectric constant and it’s function

Electric ChargeElectric 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.

Charges with the same electrical sign repel each other; and charges with opposite electrical signs attract each other.

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.

Electric Charge - Lightning

SI unit of charge: the coulomb, C. All charges are integer multiples of the charge on the electron:

Electric Charge

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 materials in which electric charges move freely

Semiconductors are intermediate; their conductivity can depend on impurities and can be manipulated by external voltages.

Insulators materials in which electric charges do not move freely.

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:

Called Coulomb’s Law

221

12 r

qkqF

221

21 r

qkqF

r

q1 q2

221

e221

e r

qkqF

r

qqF

229229

0

C/Nm1000.9C/Nm10988.84

1

k

22120 Nm/C1085.8

Electric Force

If there are multiple point charges, the force vectors must be added to get the net force.

(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?

0.3m

q2 = +2nCF12F21

q1 = -1nC

(0, -0.3m)

(0, +0.3m)

(0, 0.4m)

q1 = +2.5nC

q2 = +2.5nC

y

xq3 = +3.0nC

r31

r32

(b) What is the net electric force on q3 ?

EXAMPLE 1

Solution:

(a)

N0.2N100.2

m)3.0(

C)10C)(2101)(/CNm10(9

6-

2

9-9229

221

2112

r

qkqFF

q1 = +2.5nC

q2 = +2.5nC

y

x

F32

F31

Fnet = F3

(b)

Solution:

(b)

N0.27

m)5.0(

C)10C)(3.0105.2)(/CNm10(92

-99229

232

32

r

qkqF

r31 = r32 = 0.5m

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

3132313 2FFFF

o1 370.4m

m3.0tan

N43.0N)cos370.27(2cos22 o32313 FFF

(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 ?

EXAMPLE 2

Solution:

Given: r = 3 x 10-15m; q1=q2 = +1.6 x 10-19C ; mp = 1.67 x 10-27kg

N6.25m)10(3

C)10)(1.6/CNm10(9215-

2-19229

221

e

r

qkqF

(a) Using Coulomb’s Law;

22827-

e m/s1053.1kg101.67

25.6N

pm

Fa

272

228

1056.1m/s8.9

m/s101.53

g

a

(b)

Electric Field

The electric field at any location is

defined as follows:

The direction of the field E is the direction the force would be on a positive charge.

2

2on )/(

r

kq

q

rkqq

q

FE q

SI Unit: N/C

Electric FieldCharges create electric fields, and these fields in turn exert electric forces on other charges.

Electric field of a point charge:

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.

0.6x

0.0

q1 = +1.5μC q1 = +6μC

EXAMPLE 3

Solution

22

21

21 )(or

xd

kq

x

kqEE

212

2 )(

)/(1

xd

qq

x

xdxxd

qq

x

21

)(

/12

122

m2.03

m6.0

3

dx

Where, d is the distance of q2, rearranging this expression,

With q2/q1 = 4, taking square root of both sides:

Thus;

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

x30o

30o

30o

q1

q2

q3

d d

d

y

x+2μC +12μC

-8μC

ss

sP

2. Find the electric field at point P due to the charges shown where s = 50cm.

EXERCISE 1

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 FieldsThe 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 2Electric 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:

• When charge moves from UA to UB, energy changes• In general, electric potential energy given by

b

a

b

a

drFdrFW cos''dr = charge displacementθ = angle between F’ and drF’ =F by E, but in different direction

+Q +q E=F/q

UAUB

WUUU BA

drEqdrFU ..

r

kQqU

Electric Potential

• Definition: Electric potential energy per unit charge

• Unit: Volt or JC-1

• For a number of Q1, Q2 and Q3 at distance r1,r2 and r3 from point P

r

kQdrE

q

UV .

i

i

r

Qk

r

Q

r

Q

r

QkV )(

3

3

2

2

1

1

+Q1

P

r2

+Q2

+Q3r1r3

Electric Potential Energy & Electric Potential Difference

It takes work to move a charge against an electric field. Just as with gravity, this work increases the potential energy of the charge.

Electric Potential Energy

Gravity !!!


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.

SI unit of electric potential: Joule/Coulomb or the volt, V.

Electric potential difference


The potential difference ∆V between parallel plates can be calculated relatively easily:

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.

d – separation between two parallel plates.


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 !!!


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.

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?

EXAMPLE 4

Solution:

Given: E = 1500 N/C ; qp = +1.6 x 10-19C ; mp = 1.67 x 10-27kg ; d = 1.5 x 10-2m

J103.6m)10)(1.5C)(1500N/C101.6( -182-19 EdqU pe

V5.22C106.1

J106.319

18e

pq

UV

e2

e0

2

1

0

Uvm

UKKKKKK

UK

p

(a)

(b)

(c)

m/s1057.6)(2 4e

pm

Uv

Total energy of proton is constant

Initial, K0 = 0

∆U is negative – when its returnto negative plate


Electric potential difference of a point charge:


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.


The electric potential energy of a system of two charges is the change in electric potential multiplied by the charge.

12

2112 r

qkqU Mutual electric potential energy

(two charges)


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.

CapacitanceThe 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,

The quantity inside the parentheses is called the permittivity of free space, ε0.

or d

AC 0

Michael Faraday(1791 – 1867)British physicist

Capacitance

The energy stored in a capacitor is the energy required to charge it:

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

EXAMPLE 5

Solution:

(a)

(b)

(c)

109.36

006.0

))(0.25m10(8.854

d

AC

9

212-

o

F

m

J1066.2

V) F)(1210(36.92

1

CV2

1U

6

29-

2C

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 capacitance of a capacitor containing a dielectric is increased. The definition for capacitance is

E

E

V

V 00

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

or

is dimensionless and > 1.000

Only when the capacitor charge isconstant

DielectricsInserting 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

SUBTOPIC Charge units Electric field Electric force & Coulomb’s Law Capacitance and unit Parallel...

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Transcript of SUBTOPIC Charge units Electric field Electric force & Coulomb’s Law Capacitance and unit Parallel...