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;

**Faraday’s Law of Induction**

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

**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. - 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.