Faraday’s law - Electromagnetic Induction

Faraday’s law

Lessons

Notes:

In this lesson, we will learn:

  • Faraday’s Law
  • Faraday’s Law of Induction
  • Different methods of inducing emf.

Notes:

Faraday’s Law
  • According to Faraday the induced emf is proportional to the following factors:
      • The rate of change of magnetic flux through the loop, ϕB\phi B.
      • The loop’s area (AA) and angle (θ\theta ).

ϕB=BA=BAcosθ \phi_{B} = B_{\bot}A = BA \cos \theta

Unit: tesla.meter2 = weber \quad (1T.m2=1Wb1T.m2= 1 Wb)

BB_{\bot}: is the component of the magnetic field B\overrightarrow{B} perpendicular to the face of the loop.
θ\theta : is the angle between magnetic field B\overrightarrow{B} and a line perpendicular to the face of the loop.

Faraday's Law


Notes:
\qquad a. When the loop is parallel to B\overrightarrow{B}, θ \theta =90° and ϕB= \phi_{B} = 0

Faraday's Law


\qquad b. When the loop is perpendicular to B\overrightarrow{B}, θ \theta =0 and ϕB=BA \phi_{B} = BA

Faraday's Law

  • Number of line per unit area is proportional to the filed strength, therefore, ϕB \phi_{B} is proportional the the total number of lines passing through the loop’s area
    • When the loop is parallel to B\overrightarrow{B}, no filed line will pass through the loop, ϕB \phi_{B} =0
    • When the loop is perpendicular to B\overrightarrow{B}, maximum number of lines will pass through the loop, ϕB \phi_{B} is maximum.

    Faraday’s Law of Induction
  • The flux through the loop changes by the amount of Δϕ \Delta \phi over Δt \Delta t interval of time, therfore, the induced emf is calculated as follows;

  • ϵ= \epsilon = - ΔϕΔt \large \frac{\Delta \phi} {\Delta t}


    if the loop contains N loops, the induced emf in each loop adds up;

    ϵ=N \epsilon = -N ΔϕΔt \large \frac{\Delta \phi} {\Delta t}


Different Methods of Inducing emf.

In general, there are three different ways to change the magnetic flux;

  1. Changing B
    It could be done by changing the number of the loops, which in return changes the strength of the filed.
    More number of loops \Rightarrow larger magnetic field \Rightarrow bigger flux
    NBϕN \propto B \propto \phi

  2. Changing A
    The current can be induced by changing the area of the loop. As flux through the loop changes, the current is induced to maintain the the original flux.

  3. Faraday's Law


    Note: decreasing the area of the loop, induces a current, the induced current acts in a direction to increase the magnetic field in the original direction. Therefore, a magnetic field into the page is induced.

  4. Changing θ \theta
    • The current can be induced by rotating the coil in a magnetic field. The flux through the coil goes from maximum to zero.
Faraday's Law
  • Intro Lesson
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Faraday’s law

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