Welcome to Physics CourseWelcome to Physics Course Electromagnetic (1)

Course Code: 2210 Phy

Lecturer Dr: Asma M.Elbashire.mail asmamohammed72@yahoo.com

Introduction and Course description

Course Report

Electrical Meters1. The Galvanometer2 . The Ammeter3. The Voltmeter

The electric field and potential difference:1. Electric charge, electric force.2. Coulomb’s law.3. Electric field.4. Analysis of electric force.5. Gauss’s law and its applications.6. The Potential Energy and Potential

Difference.7. Electric Potential and Potential Energy due to

Point Charge.8. Motion of charged particle.

Lectures 1 to 4

1. Electric charge, electric force

Electrostatics

Structure of Matter• Fundamental building blocks of the

matter are atoms.

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+ ++ + -

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Structure of Matter• Neutral atom – electron = Positive ion

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+ ++ + -

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C101.602charge electron -191

Structure of Matter• Neutral atom + electron = negative

ion.

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+ ++ + -

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As an example we can take a rod of glass rubbed with silk

In reality those charges are not created but simply transferred between one piece and the other, due to the friction between the silk and the rod.

العدم من توجد ال الشحنات تلك فان ، األمر حقيقة فيببساطة وقطعة تنتقلولكن القضيب بين االحتكاك بفعل

. الحرير

Q

Q

Q

Methods of charging an objectAn object becomes electrostatically charged by

1. Friction,which transfers electrons between two objects in contact,

2. Contact with a charged body which results in the transfer of electrons,

3. Induction which produces a charge redistribution of electrons in a material.

Problem

Problem

Problem

Applications: • Charging by induction occurs during

thunderstorms. • رعدية عواصف

The negatively charged bottoms of clouds induce a positive charge on the surface of Earth below.

• Lightning البرق is an electrical discharge between a

cloud and the oppositely charged ground or between oppositely charged parts of clouds.

•Electrostatics is the study of electric charge at rest.

Fundamental ChargesNote that the electron and proton both have the same charge,

with the electron being negative and the proton being positive. This amount of charge is often called the

electronic charge, e. This electronic charge is generally considered a positive value (just like g in gravity). We add the negative sign when we need to:

qe = -e; qp = +e.

The SI unit of charge is the coulomb (C).

Properties of electric charge

1.Two kinds of charges occur in nature, positive and negative o like charges repel one another, o and unlike charges attract one another.2. Charge is conserved.3. Charge is quantized.

Two kinds electric force, 1- attractive force 2- repulsive forces, needs two kinds of

charge.

Homework

Q

Q

Q

Q

Q

Q

Q

2- Coulomb’s law.

Electric Force: Coulomb’s Law

Electric Force: Coulomb’s Law• we can express Coulomb’s law as an equation giving the

magnitude of the electric force Fe between two point charges:

Where q1 and q2 the charges, r is the distance between the charges.

ke is a constant called the Coulomb constant, it has the value

where the constant epsilon is known as the permittivity of free space

• Coulomb confirmed that: the electric force between two small charged spheres is proportional to the inverse square of their separation distance r.

Coulomb’s Law

• The electric force has the following properties:

1. is inversely proportional to the square of the separation r between the particles

2. is proportional to the product of the charges q1 and q2 3. is attractive if the charges are of opposite sign 4. is repulsive if the charges have the same sign5. is a conservative force.

• There are four fundamental forces of nature.

1. Gravitational Force2. Electromagnetic Force3. Strong Nuclear Force4. Weak Nuclear Force

4. Analysis of electric force

Problem• The average distance r between the electron and the

proton in the hydrogen atom is 5.3x10-11 m. • What is the magnitude of the average electrostatic

force that acts between these two particles?

• Solution the electrostatic force, Fe = 1 q1 q2 4o r2 = (8.99 X 109N.m2/C2)(1.60X l0-19C)2

(5.3 X 10-11 m)2

= 8.2 X 10-8 N.

Problem• The nucleus of an iron atom has a radius of about

4x10-15 m and contains 26 protons. • What repulsive electrostatic force acts between two

protons in such a nucleus if a distance of one radius separates them?

• Solution • F = 1 qp qp 4o r2

= (8.99 x l09N.m2/C2)(l.60x l0-19 C)2 (4 X l0-15)2

=14 N.

Problem

Problem

Problem

Problem

Problem

Homework

3. Electric field

Electric Field - Definition• the electric field vector E at a point in space is defined as

the electric force Fe acting on a positive test charge q0 placed at that point divided by the test charge:

Note that since F is a vector and q is a scalar, E must be a vector.the units of Electric Field in SI units of newtons per coulomb (N/C)

Electric Field Lines

• The electric field lines for a point charge. • (a) For a positive point charge, the lines are directed radially outward.• Or the electric field lines extend away from positive charge• • (b) For a negative point charge, the lines are directed radially inward. • Or the electric field lines extend towards negative charge.

The field lines for two equal positive charges

The field lines for two charges equal in magnitude but opposite in sign – an electric dipole

NB the electric field vector at a point is tangent to the field line through the point

5- Gauss’s law and its applications.

Electric Flux

• The Electric Flux is amount of electric field passing through a surface area

1. the number of field lines per unit area (the line density) is proportional to the magnitude of the electric field.

2. The total number of lines penetrating the surface is proportional to the product EA.

3. This product EA is called the electric flux E

Electric Flux• Electric flux • is proportional to the number of electric

field lines penetrating some surface.

• the SI units of electric flux (N.m2/C.)

AE AdE

Gauss’s LawGauss’s LawThe total flux passing through a closed surface is The total flux passing through a closed surface is proportional to the charge enclosed within that surface.proportional to the charge enclosed within that surface.

Note: The area vector points outwardNote: The area vector points outward

0qAdE

surfaceE

E d

A =

Qenclosed

0

Gauss’s Law

The total flux within a closed surface …

… is proportional tothe enclosed charge.

Gauss’s Law is always true, but is only useful for certain very simple problems with great symmetry.

The Gaussian Surface

The Gaussian Surface is an is an imaginary closed surface created to enable the application of Gauss’s Law

Applications of Gauss’s Law

1.The Electric Field Due to a Point Charge

Starting with Gauss’s law, calculate the electric field due to an isolated point charge q.

2. The Electric Field Due to a Thin Spherical Shell

A thin spherical shell of radius a has a total charge Q distributed uniformly over its surface .Find the electric field at points (A) outside and (B) inside the shell.

2. The Electric Field Due to a Thin Spherical Shell

the electric field at points(A)outside and

(B) (B) inside the shell.The electric field inside the spherical shell is zero.

Find the electric field a distance r from a line of positive charge of infinite length and constant charge per unitlength

Conclusions Gauss’ Law

1. Only the charge enclosed within a volume defined by a closed surface contributes to the net electric flux through the surface.

2. That net flux through the surface is proportional to the charge enclosed within the volume.

Conclusions

3. 3. Gaussian surface is an imaginary closed surface necessary to solve a problem using Gauss’s Law

4. 4. Gauss’s Law can be used to determine the electric field of a charge distribution if there is a high degree of symmetry

Conductors in Electrostatic Equilibrium• a good electrical conductor contains charges (electrons)• that are not bound to any atom and therefore are free to move about within the

material. • When there is no net motion of charge within a conductor, the conductor is in

electrostatic equilibrium.

• A conductor in electrostatic equilibrium has the following properties:• 1. The electric field is zero everywhere inside the conductor.

• 2. If an isolated conductor carries a charge, the charge resides on its surface.

• 3. The electric field just outside a charged conductor is perpendicular to the surface of the conductor and has a magnitude σ/0, where σ is the surface charge density at that point.

• 4. On an irregularly shaped conductor, the surface charge density is greatest at locations where the radius of curvature of the surface is smallest.

6- The Potential Energy and Potential Difference.

The Potential Energy and Potential Difference • The electric potential is defined to be the potential energy per unit

charge. Thus...

Electric Potential Difference is the work done moving a positive test charge between two points in an electric field divided by the magnitude of the test charge. electric potential = work done

charge

ΔV = W q

The SI unit of electric Potential Difference is Volt

A volt is a measure of the potential difference between two points.

Processes occurring during thunderstorms cause large differences in electric potential between a thundercloud and the ground.

The result of this potential difference is an electrical discharge that we call lightning, such as this display over Tucson, Arizona.

• Electron-volts• The electron-volt is a unit of energy or work. • An electron-volt (eV) is the work required• to move an electron through a potential difference of one

volt.

Since the magnitude of the charge of an electron is about1.602 × 10−19 C, it follows that an electron-volt is about

Problem

Solution

• When we have a uniform electric field, we can find ΔV where

ΔV = - E*dElectric Potential Difference in a uniform Electric Field is

equal to the product of electric field intensity and the distance moved by the charge.

Equipotentials and Electric Fields Lines of Positive Charge

1. The equipotentials for a point charge are a family of spheres centered on the point charge

2. The field lines are perpendicular to the electric potential at all points

Homework1. Draw and describe the Equipotentials and Electric

Fields Lines in case of positive charge.

unit of electric field

ΔV = - E*dE = Electric Field units Newton/Coulomb (N/C)

d = distance unit meter (m)• it follows that the SI unit of electric field (N/C) can also be

expressed in volts per meter:

Problem

Problem

7- Electric Potential and Potential Energy due to Point Charge

How electrostatic concepts are related?

• Field and Force are closely relatedBoth are vectorsF = qE

Potential and Potential Energy are closely relatedBoth are scalarsU = qV

Electric Potential Due to Point Charges

the electric potential created by a point charge is:

Electric potential due to several point charges

Problem

• A charge q1 = 2 C is located at 4m from a point P, and a charge q2 = - 6 C is located at 5 m from P.

• (A) Find the total electric potential due to these charges at the point P

Problem

Problem

• What is the electric dipole?

• An electric dipole consists of two charges of equal magnitude and opposite sign separated by a distance.

Homework

Problem Homework

8- Motion of charged particle

Motion of Charged Particles in a Uniform Electric Field

• When a particle of charge q and mass m is placed in an electric field E,

• the electric force exerted on the charge F = qE.• If this is the only force exerted on the particle, it must be

the net force and causes the particle to accelerate• according to Newton’s second law. Thus

Motion of Charged Particles in a Uniform Electric Field

• If E is uniform (constant in magnitude and direction), then the acceleration is constant.

• If the particle has a positive charge, its acceleration is in the direction of the electric field.

• If the particle has a negative charge, • its acceleration is in the direction opposite the electric field.

Motion of Charged Particles in a Uniform Electric Field

• An electron is projected horizontally into a uniform electric field produced by two charged plates.

• The electron undergoes a downward acceleration (opposite E), and

• its motion is parabolic while it is between the plates.

Homework

1. Describe how the Cathode Ray Tube (CRT) works