Welcome to Physics Course Welcome to Physics Course Electromagnetic (1) Course Code: 2210 Phy Lecturer Dr: Asma M.Elbashir e.mail

Introduction and Course description

Course Report Electrical Meters 1.The Galvanometer 2. The Ammeter 3. 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

Structure of Matter Neutral atom – electron = Positive ion

Structure of Matter Neutral atom + electron = negative ion

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. في حقيقة الأمر ، فان تلك الشحنات لا توجد من العدم ولكن ببساطة تنتقل بفعل الاحتكاك بين القضيب وقطعة الحرير.

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Methods of charging an object An 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

Applications: Charging by induction occurs during thunderstorms. عواصف رعدية 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 Charges Note 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: q e = -e; q p = +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 olike charges repel one another, oand 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

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2- Coulomb’s law.

Electric Force: Coulomb’s Law

we can express Coulomb’s law as an equation giving the magnitude of the electric force F e between two point charges: Where q 1 and q 2 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 sign 5.is a conservative force.

There are four fundamental forces of nature. 1.Gravitational Force 2.Electromagnetic Force 3.Strong Nuclear Force 4.Weak Nuclear Force 4. Analysis of electric force

Problem The average distance r between the electron and the proton in the hydrogen atom is 5.3x m. What is the magnitude of the average electrostatic force that acts between these two particles? Solution the electrostatic force, F e = 1 q 1 q 2 4  o r 2 = (8.99 X 10 9 N.m 2 /C 2 )(1.60X l0 -19 C) 2 (5.3 X m) 2 = 8.2 X N.

Problem The nucleus of an iron atom has a radius of about 4x 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 q p q p 4  o r 2 = (8.99 x l0 9 N.m 2 /C 2 )(l.60x l0 -19 C) 2 (4 X l0 -15 ) 2 =14 N.

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Homework

3. Electric field

Electric Field - Definition the electric field vector E at a point in space is defined as the electric force F e acting on a positive test charge q 0 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.m 2 /C.)

Gauss’s Law The total flux passing through a closed surface is proportional to the charge enclosed within that surface. Note: The area vector points outward

Gauss’s Law The total flux within a closed surface … … is proportional to the enclosed charge. Gauss’s Law is always true, but is only useful for certain very simple problems with great symmetry.

The Gaussian Surface is an The Gaussian Surface 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 unit length

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 Gaussian surface is an imaginary closed surface necessary to solve a problem using Gauss’s Law 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 about × 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*d Electric 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

Homework 1.Draw and describe the Equipotentials and Electric Fields Lines in case of positive charge.

unit of electric field ΔV = - E*d E = 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

7- Electric Potential and Potential Energy due to Point Charge

How electrostatic concepts are related? Field and Force are closely related Both are vectors F = qE Potential and Potential Energy are closely related Both are scalars U = 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 q 1 = 2  C is located at 4m from a point P, and a charge q 2 = - 6  C is located at 5 m from P. (A) Find the total electric potential due to these charges at the point P 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