# Faraday’s law - Electromagnetic Induction

#### Electromagnetic Induction Topics:

###### 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 ($\theta$). $\phi_{B} = B_{\bot}A = BA \cos \theta$Unit: tesla.meter2 = 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. Faraday’s Law of Induction 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; $\epsilon = -$ $\large \frac{\Delta \phi} {\Delta t}$ if the loop contains N loops, the induced emf in each loop adds up; $\epsilon = -N$ $\large \frac{\Delta \phi} {\Delta t}$ Different Methods of Inducing emf. 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. 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. 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.  