# Faraday's Law: Unlocking the Power of Electromagnetic Induction Dive into the fascinating world of Faraday's Law. Discover how changing magnetic fields induce electric currents, powering modern technology from generators to wireless charging.

Now Playing:Faradays law – Example 0a
Intros
Examples
1. Four conductors of different lengths are moved through a uniform magnetic field at the same speed. Which conductor will induce the greatest emf?
Induced EMF and Lenz’s law
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.
Concept

Welcome to our exploration of Faraday's law, a fundamental principle in electromagnetism that revolutionized our understanding of electricity and magnetism. This law, discovered by Michael Faraday in 1831, explains the phenomenon of electromagnetic induction. It describes how a changing magnetic field can induce an electric current in a nearby conductor. To kick off our learning journey, I've prepared an introduction video that visually demonstrates this concept. This video is crucial as it breaks down the complex ideas into easily digestible parts, making Faraday's law more accessible. You'll see real-life applications and experiments that showcase the law in action. As we progress, we'll delve deeper into the mathematical formulations and practical implications of Faraday's law. Remember, this principle underpins much of our modern technology, from electric generators to transformers. So, let's get started and unravel the mysteries of electromagnetic induction together!

FAQs
1. #### What is Faraday's Law of Electromagnetic Induction?

Faraday's Law states that the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop. It's expressed mathematically as ε = -dΦ/dt, where ε is the induced EMF and dΦ/dt is the rate of change of magnetic flux.

2. #### How does changing the loop's area affect induced EMF?

Changing the loop's area affects the amount of magnetic flux passing through it. Increasing the area exposed to the magnetic field will increase the induced EMF, as more magnetic field lines can pass through the larger area. This principle is utilized in the design of electric generators and transformers to maximize efficiency.

3. #### What are some practical applications of Faraday's Law?

Faraday's Law has numerous practical applications, including:

• Electric generators for power production
• Transformers in power distribution systems
• Induction cooktops for efficient cooking
• Electromagnetic flow meters for measuring conductive liquid flow
• Wireless charging technology for electronic devices
4. #### How does the angle between magnetic field lines and the loop affect induced EMF?

The angle between magnetic field lines and the loop's normal affects the magnetic flux. Maximum EMF is induced when the field lines are perpendicular to the loop's surface (θ = 0°, cos θ = 1). When the field lines are parallel to the surface (θ = 90°, cos θ = 0), no EMF is induced. This relationship is described by the equation Φ = BA cos θ, where Φ is magnetic flux, B is magnetic field strength, A is loop area, and θ is the angle.

The negative sign in Faraday's Law equation (ε = -dΦ/dt) represents Lenz's Law. It indicates that the induced current flows in a direction that opposes the change in magnetic flux that caused it. This opposition is nature's way of conserving energy and maintaining equilibrium. Understanding this concept is crucial for predicting the behavior of induced currents in various electromagnetic applications.

Prerequisites

Faraday's law is a fundamental principle in electromagnetism, but to truly grasp its significance, it's crucial to have a solid understanding of several prerequisite topics. These foundational concepts provide the necessary context and background knowledge to fully appreciate the intricacies of Faraday's law.

One of the key prerequisites is understanding the rate of change. This mathematical concept is essential when dealing with Faraday's law, as it directly relates to the rate of change of magnetic flux. In Faraday's law, we're concerned with how quickly the magnetic field is changing, which is why a strong grasp of rate of change is crucial. It allows us to quantify and analyze the variations in magnetic flux over time, a cornerstone of electromagnetic induction.

Another vital prerequisite topic is the magnetic field due to a long straight wire & force between two parallel wires. This concept provides the foundation for understanding how magnetic fields behave and interact. When studying Faraday's law, we often deal with loops of wire in magnetic fields. Knowing how the angle between the magnetic field and the loop affects the induced current is crucial. This prerequisite topic helps build that understanding, making it easier to visualize and calculate the effects described by Faraday's law.

Lastly, familiarity with electric generators & counter EMF (Back EMF) is incredibly beneficial when delving into Faraday's law. Electric generators are practical applications of Faraday's law, demonstrating how changing magnetic fields can induce electrical currents. Understanding the principles behind generators provides real-world context for Faraday's law and helps illustrate its importance in modern technology. Additionally, the concept of counter EMF, or back EMF, is directly related to Lenz's law, which is often studied alongside Faraday's law and helps explain the direction of induced currents.

By mastering these prerequisite topics, students can approach Faraday's law with a more comprehensive understanding. The rate of change concept provides the mathematical tools, the understanding of magnetic fields offers the physical framework, and knowledge of electric generators gives practical context. Together, these prerequisites create a solid foundation upon which a deeper understanding of Faraday's law can be built, enabling students to better grasp its implications and applications in the field of electromagnetism.