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 02: Electric Field » 2.2 Electric Field of a Point Charge

2.2 Electric Field of a Point Charge

2.2 Electric Field of a Point Charge from Office of Academic Technologies on Vimeo.

2.2 Electrical Field of a Point Charge

Now let us try to determine the electric field for point charge. Let’s assume that our source charge is a positive point charge q and we are interested to determine the electric field some r distance away at point p. In order to do this, we will choose a positive test charge q zero and place it at the point of interest.

Since both of these charges are like charges, our source will repel the test charge q zero in radially outward direction with a Coulomb force of f sub c. Now we know that the electric field that it generates at the point of interest should be the same direction with the Coulomb force.

In other words it has to be radially outward direction. The magnitude of this force is from Coulomb’s law, 1 over 4 Pi Epsilon zero times the product of the magnitude of the charges, q q zero over r squared.

If we’d like to express this in vector form, then we can introduce a unit vector in radial direction denoted as r unit and multiply the magnitude of this force by that unit vector r. From the definition of electric field, we have electric field is equal to Coulomb force per unit charge. In this case, per unit test charge.

Substituting the explicit value of Coulomb force, we will have 1 over 4 Pi Epsilon zero q q zero over r squared times r unit divided by q zero. Q zeroes at the numerator and the denominator will cancel, leaving us electric field of a point charge is equal to 1 over 4 Pi Epsilon zero charge divided by the square of the distance to the point of interest.

Therefore if we are interested with the electric field generated by a point charge q some r distance away from the charge at a point p, that electric field is going to be in radially outward direction. Its magnitude is going to be equal to Coulomb constant times magnitude of the charge q divided by square of the distance to the point of interest. R is the distance between the source charge and point of interest.

The expression over here in the box is also sometimes known as Coulomb’s law in terms of electric field. Now, if we have more than one point charges in our system and if we are interested in the net electric field at a specific point for more than one point charges, then simply we calculate the electric field due to each one of these charges at the point of interest and then add these electric field vectors vectorially to be able to get the total electric field.

Therefore e total, or the net electric field at the point of interest will be the vector sum of the electric fields generated by each individual charge at the point of interest. Following example is going to be related to the superposition of the electric field vectors.

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