Faraday’s law

In this lesson, we will learn:

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

• 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 ($\theta$).

• 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;

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

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
   $N \propto B \propto \phi$


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.



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.


3. 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.