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, $\phi B$.
 The loop’s area ($A$) and angle ($\theta$).
Unit: tesla.meter^{2} = weber $\quad$ ($1T.m2= 1 Wb$)
$B_{\bot}$: is the component of the magnetic field $\overrightarrow{B}$ perpendicular to the face of the loop.
$\theta$: is the angle between magnetic field $\overrightarrow{B}$ and a line perpendicular to the face of the loop.
Notes:
$\qquad$ a. When the loop is parallel to $\overrightarrow{B}$, $\theta$ =90° and $\phi_{B} =$ 0
$\qquad$ b. When the loop is perpendicular to $\overrightarrow{B}$, $\theta$ =0 and $\phi_{B} = BA$
 Number of line per unit area is proportional to the filed strength, therefore, $\phi_{B}$ is proportional the the total number of lines passing through the loop’s area
 When the loop is parallel to $\overrightarrow{B}$, no filed line will pass through the loop, $\phi_{B}$=0
 When the loop is perpendicular to $\overrightarrow{B}$, maximum number of lines will pass through the loop, $\phi_{B}$ is maximum.
 The flux through the loop changes by the amount of $\Delta \phi$ over $\Delta t$ interval of time, therfore, the induced emf is calculated as follows;
if the loop contains N loops, the induced emf in each loop adds up;
In general, there are three different ways to change the magnetic flux;
 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
$N \propto B \propto \phi$  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.  Changing $\theta$
 The current can be induced by rotating the coil in a magnetic field. The flux through the coil goes from maximum to zero.
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.

Intro Lesson