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 » 1.2 Electrical Interactions

1.2 Electrical Interactions

For demonstrations, see:
http://maxwell.uncc.edu/aktas/PHYS2102nline/PHYS2102EandM.html

1.2 Electrical Interactions

Electromagnetic interactions are going to be this subject of interactions for this semester. We will study the cause of these interactions, property of matter which is responsible for these interactions. We will study the forces associated with these interactions.

Starting from the early Greek philosophers’ times, it was observed that, if you rubbed a piece of amber it will attract bits of straw. This ancient observation is a direct ancestor of the electronic agent which we live today.

The Greeks also recorded the observation that some naturally occurring stones which we know them today as mineral, magnetite will attract iron.

Starting from these two modest origins, electricity and magnetism dual up as two different branches of physics. But as the scientists observe these phenomenon they also recorded parallels between these two interactions, and they always looked for a link between electricity and magnetism.

That link though has not been established until 1820, as a result of an accidental discovery by Hans Christian Oersted which he showed that electric current in a wire can deflect a magnetic compass needle and this was the first link between electricity and magnetism.

Since that time, these two branches of physics joined together as electricity and magnetism and doubled up and it became one of the best established theories of physics. And we take the advantage of this area, or this branch, of physics today in every aspect of our lives, as a matter of fact; one cannot imagine a lifestyle today without the electricity.

By studying these interactions we will first concentrate on the electrical part of these interactions by looking at some interesting observations that we experience almost on a daily basis.

So, if we just start with the electrical interactions. It is almost everyone’s experience that if you walk over the carpet on a dry day and then try to touch the metal knob of a door, we can feel a little pain in your fingertip, as a matter of fact you can do this during night, during dark, you can see a spark going from your fingertip to the door knob or vice versa.

Or if you have a long hair and if you comb it on a dry day again you will see that after certain tries your hair will fly apart. And again if you hold that comb after you brush your hair nearby to a piece of paper you will see that the comb will attract the other pieces of paper.

Of course a spectacular observation of the similar type of phenomenon occurs during the thunderstorms, which is lightening.

The origin of all of these interesting phenomena is basically the same. As a matter of fact, if we consider a simple experiment by setting up a pendulum, which consists of a plastic strip suspended by a light string and another plastic strip, identical plastic strip, which is held next to the pendulum.

Of course when the objects are in this position we are not going able to detect a specific interaction taking place in this system. Although they attract one another with the gravitational force, but since they are basically standing next to a very massive object which is earth and its gravitational pull is much much greater than the gravitational force that these two plastic strips exert one another, we will not able to observe a specific change in the system when we hold these two objects nearby to one another.

But if you take the same system and rub these plastics strips both pendulum and the other one with wool cloth and then hold them nearby to each other we will see that the pendulum will swing away from the fixed plastic rod. Of course for this to happen, pendulum had to be repelled by the fixed plastic rod. In other words, it had to the influence of a force pushing the pendulum away from the fixed plastic strip. Therefore, this happens after rubbing the plastic strip with wool cloth.

Of course from Newton’s action reaction principle after this rubbing process, pendulum also exerts similar magnitude of force in opposite direction to the fixed plastic rod.

Now, let’s look at another case with a different similar type of experiment with a different type of pair of objects. In this case, let’s consider our pendulum consists of a glass strip and sitting again next to a fixed identical glass strip. Again, in the first case we are not going to be able to observe any interaction which is taking place between with these two objects.

But now, let us rub the glass with a silk cloth and as well as the pendulum and hold them nearby as in the previous case. In this case also we will observe that the pendulum will swing away from the fixed glass strip, again indicating the existence of a repulsive force generated by the fixed glass strip over the pendulum. And this will be the case after rubbing with silk cloth, in this case.

Now, one interesting observation can be made by comparing the plastic strip or pendulum with the glass strip or pendulum after the rubbing processes. For example, let’s say we take the glass strip after it is being rubbed, after rubbing with silk cloth, and hold it nearby to the plastic pendulum which is rubbed with wool cloth.

Now you will observe that the pendulum is going to be attracted by the glass strip, in other words, the plastic pendulum, after rubbing with wool cloth will be attracted by the glass strip which has rubbed with silk cloth, indicating that the pendulum is going to be attracted by the glass of a certain magnitude, certain amount of force which will cause the pendulum to now swing towards the glass strip.

These simple observations will show us that something which is taking place, a certain interaction, is taking place after the rubbing processes. The associated force has two different natures. For one case it is repulsive and for the other case it is an attractive one.

The property of matter which is responsible for these interactions is called, electric charge. Our simple charge, which we will denote this by either small q, or capital Q, and we will define it as the property of matter which is responsible for electrical interactions.

At this point let’s just go ahead and introduce the unit of electric charge also, the unit of charge in SI unit system is called, Coulomb.

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