Physics for Science & Engineering II
Physics for Science & Engineering II
By Yildirim Aktas, Department of Physics & Optical Science
  • Online Lectures
    • Original Online Lectures
  • Lecture Notes
  • Exams
  • Feedback
  • Department of Physics and Optical Science

  • Announcements
  • Introduction
  • Syllabus
  • Online Lectures
    • 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
  • Homework
  • Exams
  • Lecture Notes
  • Feedback

Links

  • Department of Physics and Optical Science
  • Khan Academy
Online Lectures » Chapter 09: Induction » 9.1 Magnetic Flux, Fraday’s Law and Lenz Law » Example: Changing Magnetic Flux

Example: Changing Magnetic Flux

from Office of Academic Technologies on Vimeo.

Example- Changing Magnetic Flux

We have seen that if the magnetic flux through an area surrounded by a conducting loop is changing then, from Faraday’s law, we end up with an induced electromotive force along that loop. The Faraday’s law was given as that this induced EMF or electromagnetic force is equal to negative rate of change of magnetic flux. We said that the negative sign appears from Lenz’s law and it simply states that the associated induced current shows up along this closed conducting loop once the magnetic flux is changing through the area surrounded by that loop in such a way that it opposes its cause.

If we look at the magnetic flux, which is basically magnetic field vector dotted with area vector from the general definition of flux of any vector of quantity, change in magnetic flux occurs — let’s call that change as ΔΦB — if a change in magnetic field occurs, then we’re going to end up with a change in flux or magnetic field might remain constant, but the area that we’re dealing might change, which will result, again, with a change in flux or both of these quantities might change. In everyone of these cases, we end up with a change in flux. Therefore, it will result with an induced electromotive force and associated induced current along the closed conducting loop.

Let’s consider a simple example. Let’s assume that in a given system, the flux is changing as a function of time and that is given in explicit form as 8t3 plus 6t2 plus 7 webers. Therefore the flux, which is varying relative to this mathematical function as a function of time in this manner, and if we’re interested to find out the induced electromagnetic force, that will be equal to – dΦB over dt, which is going to be equal to minus, if you take the derivative of this function with respect of time we will have 24t2 plus 12t and the derivative of the last term, since it is a constant, will be equal to 0. So, the induced electromagnetic force is going to be also changing as a function of time given by this quantity.

If we’re interested with the induced electromotive force at t is equal to 2 seconds, then we can easily calculated the magnitude of this induced electromotive force by substituting 24t for the first term. Therefore we will have square of 2 times 24, and plus for the second term we will have 12 times 2. Therefore the induced electromotive force is going to be equal to 2 times 24 will give us 96, plus 2 times 12 is 24, and if you add these quantities we will end up with 120 volts.

Leave a Reply Cancel reply

You must be logged in to post a comment.

Skip to toolbar
  • Log In