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##### Intros
###### Lessons
3. Different methods of inducing emf.
##### Examples
###### Lessons
1. Four conductors of different lengths are moved through a uniform magnetic field at the same speed. Which conductor will induce the greatest emf? 1. A part of a coil wire is placed in a uniform magnetic field as shown. Which two directions of motion would immediately induce an emf in the coil? 1. 1 and 2
2. 1 and 3
3. 2 and 3
4. 2 and 4
1. The diagram below shows an aluminum ring and the current induced in it by the nearby magnet that is free to move along its central axis. The magnet must be:
1. stationary
2. moving to the left
3. moving to the right
4. spinning about its central axis.
1. The diagram below shows two coils in a magnetic field. An electric current can be induced in the coil oriented with its plane.
1. parallel to a constant magnetic field.
2. parallel to a changing magnetic field.
3. perpendicular to a constant magnetic field.
4. perpendicular to a changing magnetic field.
1. A metal block moves with a constant speed in a uniform magnetic field. Which side of the block is positive?
1. JK
2. KL
3. LM
4. MJ
###### Topic Notes

In this lesson, we will learn:

• Different methods of inducing emf.

Notes:

• 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.

• 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;

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.

3. 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 $\theta$
• The current can be induced by rotating the coil in a magnetic field. The flux through the coil goes from maximum to zero. 