SUBTOPIC Charge units Electric field Electric force & Coulombs - - PowerPoint PPT Presentation

SUBTOPIC

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

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.

Charges with the same electrical sign repel each other; and charges with

• pposite electrical signs attract each other.

Electric Charge

Is an intrinsic characteristic of the fundamental particles making up those

• bjects; 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

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 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 Called Coulomb’s Law

r q1 q2

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 = +2nC F12 F21 q1 = -1nC

y

• (0, -0.3m)

(0, +0.3m) (0, 0.4m) q1 = +2.5nC q2 = +2.5nC y x q3 = +3.0nC r31 r32

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

Solution:

(a)

N 0.2 N 10 0.2 m) 3 . ( C) 10 C)(2 10 1 )( /C Nm 10 (9

6

• 2

9

• 9

2 2 9 2 2 1 21 12

µ = × = × × × = = =

−

r q kq F F

y q1 = +2.5nC q2 = +2.5nC y x F32 F31

θ θ

Fnet = F3 (b)

Solution:

(b)

N 0.27 m) 5 . ( C) 10 C)(3.0 10 5 . 2 )( /C Nm 10 (9

2

• 9

9 2 2 9 2 3 2 32

µ = × × × = =

−

r q kq F

r31 = r32 = 0.5m Taking into account the direction of F31 and F32 is symmetry – then y – components 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

31 32 31 3

2F F F F = + =

• 1

37 0.4m m 3 . tan =

• =

−

θ

N 43 . N)cos37 0.27 ( 2 cos 2 2

• 32

31 3

µ µ θ = = = = F F F

(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. a) 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

N 6 . 25 m) 10 (3 C) 10 )(1.6 /C Nm 10 (9

2 15

• 2
• 19

2 2 9 2 2 1 e

= × × × = = r q kq F

(a) Using Coulomb’s Law;

2 28 27

• e

m/s 10 53 . 1 kg 10 1.67 25.6N × = × = =

p

m F a

27 2 2 28

10 56 . 1 m/s 8 . 9 m/s 10 1.53 × = × = g a

(b)

Electric Field

The electric field at any location is defined as follows:

2 2

• n

) / ( r kq q r kqq q F E

q

= = =

+ + + +

SI Unit: N/C The direction of the field E is the direction the force would be on a positive charge.

r q q

+ +

Electric Field

Charges create electric fields, and these fields in turn exert electric forces on

• ther 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. x q1 = +1.5μC q1 = +6μC

• 0.6

x 0.0

Solution

2 2 2 1 2 1

) (

• r

x d kq x kq E E − = =

2 1 2 2

) ( ) / ( 1 x d q q x − =

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

) ( x d x −

x d x x d q q x − =

• −

= 2 1 ) ( / 1

2 1 2 2

m 2 . 3 m 6 . 3 = = = d x

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 x 30o 30o 30o q1 q2 q3 d d d

• y

x +2μC +12μC

• 8μC

s s s P

• 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. 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 & 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 a b a

dr F dr F W θ cos ' '

dr = charge displacement θ = angle between F’ and dr F’ =F by E, but in different direction +Q +q E=F/q

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

+Q +q E=F/q UA UB

W U U U

B A

= − = ∆ −

• =

= dr E q dr F U . .

r kQq U =

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 kQ dr E q U V = = =

• .

point P

• =

+ + =

i i

r Q k r Q r Q r Q k V ) (

3 3 2 2 1 1

+Q1 P r2 +Q2 +Q3 r1 r3

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 !!!

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: 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.

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 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

• (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

J 10 3.6 m) 10 )(1.5 C)(1500N/C 10 1.6 (

• 18

2

• 19

× + = × × + = = ∆ Ed q U

p e

V 5 . 22 C 10 6 . 1 J 10 6 . 3

19 18 e

+ = × + × + = ∆ = ∆

− − p

q U V

(a) (b)

e 2 e

2 1 U v m U K K K K K K U K

p

∆ − = ∆ − = = ∆

• =

− = ∆ = ∆ + ∆

(c)

m/s 10 57 . 6 ) ( 2

4 e

× = ∆ − =

p

m U v

Total energy of proton is constant Initial, K0 = 0 ∆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 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.

q kq

12 2 1 12

r q kq U =

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

• r

d A C ε =

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

Solution:

(a) (b)

10 9 . 36 006 . ) )(0.25m 10 (8.854 d A C

9 2 12

• F

m

−

× = × = = ε CV 1 U

2

=

(b) (c)

J 10 66 . 2 V) F)(12 10 (36.9 2 1 CV 2 1 U

6 2 9

• 2

C −

× = × = =

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 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

• ne 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, κ.

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

E E V V

0 =

= κ

The dielectric creates a ‘reverse’ electric field – that partially cancels the field between the plates. The κ 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 Only when the capacitor charge is constant

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

• r

κ is dimensionless and > 1.000

Dielectrics

Inserting a dielectric into a capacitor while either the voltage

• r the charge is held constant has

the same effect – the ratio of charge to voltage increases. Voltage drops Voltage drops Stored energy decrease Charge on a plates increase More energy stored in capacitor