Physics for Science & Engineering II
Physics for Science & Engineering II
By Yildirim Aktas, Department of Physics & Optical Science
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  • Introduction
  • Syllabus
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    • Chapter 01: Electric Charge
      • 1.1 Fundamental Interactions
      • 1.2 Electrical Interactions
      • 1.3 Electrical Interactions 2
      • 1.4 Properties of Charge
      • 1.5 Conductors and Insulators
      • 1.6 Charging by Induction
      • 1.7 Coulomb Law
        • Example 1: Equilibrium Charge
        • Example 2: Three Point Charges
        • Example 3: Charge Pendulums
    • Chapter 02: Electric Field
      • 2.1 Electric Field
      • 2.2 Electric Field of a Point Charge
      • 2.3 Electric Field of an Electric Dipole
      • 2.4 Electric Field of Charge Distributions
        • Example 1: Electric field of a charged rod along its Axis
        • Example 2: Electric field of a charged ring along its axis
        • Example 3: Electric field of a charged disc along its axis
        • Example 4: Electric field of a charged infinitely long rod.
        • Example 5: Electric field of a finite length rod along its bisector.
      • 2.5 Dipole in an External Electric Field
    • Chapter 03: Gauss’ s Law
      • 3.1 Gauss’s Law
        • Example 1: Electric field of a point charge
        • Example 2: Electric field of a uniformly charged spherical shell
        • Example 3: Electric field of a uniformly charged soild sphere
        • Example 4: Electric field of an infinite, uniformly charged straight rod
        • Example 5: Electric Field of an infinite sheet of charge
        • Example 6: Electric field of a non-uniform charge distribution
      • 3.2 Conducting Charge Distributions
        • Example 1: Electric field of a concentric solid spherical and conducting spherical shell charge distribution
        • Example 2: Electric field of an infinite conducting sheet charge
      • 3.3 Superposition of Electric Fields
        • Example: Infinite sheet charge with a small circular hole.
    • Chapter 04: Electric Potential
      • 4.1 Potential
      • 4.2 Equipotential Surfaces
        • Example 1: Potential of a point charge
        • Example 2: Potential of an electric dipole
        • Example 3: Potential of a ring charge distribution
        • Example 4: Potential of a disc charge distribution
      • 4.3 Calculating potential from electric field
      • 4.4 Calculating electric field from potential
        • Example 1: Calculating electric field of a disc charge from its potential
        • Example 2: Calculating electric field of a ring charge from its potential
      • 4.5 Potential Energy of System of Point Charges
      • 4.6 Insulated Conductor
    • Chapter 05: Capacitance
      • 5.01 Introduction
      • 5.02 Capacitance
      • 5.03 Procedure for calculating capacitance
      • 5.04 Parallel Plate Capacitor
      • 5.05 Cylindrical Capacitor
      • 5.06 Spherical Capacitor
      • 5.07-08 Connections of Capacitors
        • 5.07 Parallel Connection of Capacitors
        • 5.08 Series Connection of Capacitors
          • Demonstration: Energy Stored in a Capacitor
          • Example: Connections of Capacitors
      • 5.09 Energy Stored in Capacitors
      • 5.10 Energy Density
      • 5.11 Example
    • Chapter 06: Electric Current and Resistance
      • 6.01 Current
      • 6.02 Current Density
        • Example: Current Density
      • 6.03 Drift Speed
        • Example: Drift Speed
      • 6.04 Resistance and Resistivity
      • 6.05 Ohm’s Law
      • 6.06 Calculating Resistance from Resistivity
      • 6.07 Example
      • 6.08 Temperature Dependence of Resistivity
      • 6.09 Electromotive Force, emf
      • 6.10 Power Supplied, Power Dissipated
      • 6.11 Connection of Resistances: Series and Parallel
        • Example: Connection of Resistances: Series and Parallel
      • 6.12 Kirchoff’s Rules
        • Example: Kirchoff’s Rules
      • 6.13 Potential difference between two points in a circuit
      • 6.14 RC-Circuits
        • Example: 6.14 RC-Circuits
    • Chapter 07: Magnetism
      • 7.1 Magnetism
      • 7.2 Magnetic Field: Biot-Savart Law
        • Example: Magnetic field of a current loop
        • Example: Magnetic field of an infinitine, straight current carrying wire
        • Example: Semicircular wires
      • 7.3 Ampere’s Law
        • Example: Infinite, straight current carrying wire
        • Example: Magnetic field of a coaxial cable
        • Example: Magnetic field of a perfect solenoid
        • Example: Magnetic field of a toroid
        • Example: Magnetic field profile of a cylindrical wire
        • Example: Variable current density
    • Chapter 08: Magnetic Force
      • 8.1 Magnetic Force
      • 8.2 Motion of a charged particle in an external magnetic field
      • 8.3 Current carrying wire in an external magnetic field
      • 8.4 Torque on a current loop
      • 8.5 Magnetic Domain and Electromagnet
      • 8.6 Magnetic Dipole Energy
      • 8.7 Current Carrying Parallel Wires
        • Example 1: Parallel Wires
        • Example 2: Parallel Wires
    • Chapter 09: Induction
      • 9.1 Magnetic Flux, Fraday’s Law and Lenz Law
        • Example: Changing Magnetic Flux
        • Example: Generator
        • Example: Motional emf
        • Example: Terminal Velocity
        • Simulation: Faraday’s Law
      • 9.2 Induced Electric Fields
      • Inductance
        • 9.3 Inductance
        • 9.4 Procedure to Calculate Inductance
        • 9.5 Inductance of a Solenoid
        • 9.6 Inductance of a Toroid
        • 9.7 Self Induction
        • 9.8 RL-Circuits
        • 9.9 Energy Stored in Magnetic Field and Energy Density
      • Maxwell’s Equations
        • 9.10 Maxwell’s Equations, Integral Form
        • 9.11 Displacement Current
        • 9.12 Maxwell’s Equations, Differential Form
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Online Lectures » Chapter 01: Electric Charge » 1.4 Properties of Charge

1.4 Properties of Charge

For example demonstrations, see:

http://maxwell.uncc.edu/aktas/PHYS2102nline/PHYS2102EandM.html

1.4 Properties of Change

. . . in light of the previous section, therefore we can express the first property of electric charge as, the like charges repel, unlike charges attract each other.

To be able to understand the mechanism which is taking place during the rubbing process causing the matter to be charged, one has to look at the matter from the atomic point of view. When we look at the atom through its simplest model, which is known as the Planetary Model, and it is called this way because when we consider the planetary system we observe the sun and the planets which are orbiting about the sun.

The planets go along their unique orbits about the sun due to the gravitational attractive force generated by the sun, which continuously pull the planets towards itself and therefore the necessary centripetal force is generated and the planets go along those unique orbits.

When we consider the atom in a similar way we see a very small tiny region, which consists of two different types of major particles. One type is positively charged, which is called proton and the other type is electrically neutral, which is called neutron. These particles are held in a very, very small tiny region which is about 10 to the minus 14 meters of diameter and it is call nucleus of the atom.

Once we leave the nucleus then we see a huge empty space, mainly, and then we see very small light particles orbiting about the nucleus of the atom. These particles are negatively charged and they are called electrons.

As the electrons orbit along some unique orbits to keep them to go along these orbits the necessary centripetal force now is generated because of the attractive force between the positively charged nucleus and negatively charged electrons. In other words, in this case the positive nucleus attracts the negatively charged electrons towards itself, therefore keeping them to go along these unique orbits.

Although this is not the actual model of the atom, it provides an excellent model to be able to explain many phenomena, and since, again, as we can easily see now it’s very similar structure-wise to the planetary system. This model is known as the planetary model of the atom.

An atom under normal conditions always tends to be electrically neutral. In other words, it contains equal amount of negative charge to that of positive charge. The magnitude of the charge on the proton is equal to the magnitude of the charge on the electron. And if we denote this by e magnitude the charge on an electron is a fundamental charge, because the electron itself is a fundamental particle and so far nobody has been able to break the electron into smaller particles.

The magnitude of the electron charge is 1.6 times 10 to the minus 19 Coulombs, in the S.I. unit system. Therefore under normal conditions an atom will always tend to be neutral. It will contain equal numbers of electrons and protons.

Well, if you rub two objects to one another at the end we will see that the electron layers of the atoms of those two objects are rubbing to each other. If we have a suitable atomic structure then we can easily transfer an electron from one atom to the other one. Let’s say that this is our Atom Number 1 and this is our Atom Number 2 and assume that this atom had two electrons originally. Of course it will have two protons in its nucleus to be able to be neutral.

But if it transfer, and our other atom has, let’s see, one proton and one electron originally, and after the rubbing process if you strip off one electron from Atom Number 1 and transfer it into Atom Number 2 then Atom Number 2 will end up with one excess unit of negative charge due to this extra electron, therefore it is going to get charged negatively, negative one unit. Whereas the other one, which will lose one of its electrons over here by transferring it to Atom Number 2 will lack one negative charge and since it has positive two units of positive charge in its nucleus therefore it will automatically get charged positively.

So as a result of the rubbing process, by stripping off electrons from one set of atoms and transferring in to the other set of atoms we cause charge imbalance while the atoms which are giving off the electrons, getting charged positively, the ones which are taking those electrons ends up having extra negative charges therefore they get negatively charged.

Well, when we look at these processes, of course this electronic exchange is taking place between two substances that they have suitable atomic structure such that they can exchange electrons. If you consider the original pair of objects that we observed before and after the rubbing process.

In the case of, for example, a glass strip and a silk cloth that before the rubbing process these two objects were neutral. And after the rubbing process the glass atoms are getting stripped of a bunch of electrons, that they are transferred to the silk cloth causing the silk cloth to be charged some minus q Coulombs. And because of lacking of some electrons causing the glass strip to get charged plus q Coulombs.

Now before the rubbing process these two objects were neutral and after the rubbing process, because of the electron exchanged one of them gets charged positively and the other one is charged negatively. But when we look at the overall charge of the system, again, we will see that after the rubbing process the total charge of the system will be the plus q plus minus q and they will cancel. Again it will end up to neutral. So when we consider the system as a whole we see that the total number of charges will be conserved.

Therefore that brings us to the second property of the electron electric charge. It simply states that, for an isolated system the total charge of the system is always conserved, no matter what type of charge exchange takes place within the system.

So, in other words, if we start with a system with a net charge of, let’s say, five Coulombs and as long as the system is isolated, in other words, there’s no charge exchange within the system and the environment. No matter what type of charge exchanges take place within that system the net charge of the system remains always as five Coulombs. This is known as The Conservation of Charge Principal. Conservation of Charge.

Since the electron is a fundamental particle the charge associated with the electron is also a fundamental charge. We now know that the atoms are getting electrically charged therefore the matter is a result of electron exchange between atoms and since electron can be transferred as a whole from one atom to the other atom, therefore the charge can always be expressed as the integer multiples of the electron charge. This is known as the quantization of the electric charge.

In order words, it simply states that the magnitude of any charge in nature can be expressed as the integer multiples of the magnitude of the electron charge. So we can express the third property as charge is quantized and if magnitude of Q represents the charge or, let’s say, any charge magnitude in nature this quantity can be expressed as integer multiples of the magnitude of electron charge where n can take values of one, two, three, and so on and so forth.

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