Electromagnetic Induction Unit 19 PDF

# Unit 19 Electromagnetic Induction ## Teaching Periods: 16 ## Weightage: 11% The Zorlu Energy Power Project is a wind farm situated in Jhimpir, Thatta District, in the Sindh province of Pakistan. This project, Pakistan's first wind farm, has gained global recognition. Wind power relies on electr...

# Unit 19 Electromagnetic Induction ## Teaching Periods: 16 ## Weightage: 11% The Zorlu Energy Power Project is a wind farm situated in Jhimpir, Thatta District, in the Sindh province of Pakistan. This project, Pakistan's first wind farm, has gained global recognition. Wind power relies on electromagnetic induction to generate electricity. In this unit, students should be able to: - Describe the production of electricity by magnetism. - Explain that induced e.m.f can be generated in two ways: - By relative movement (the generator effect) - By changing a magnetic field (the transformer effect) - Infer the factors affecting the magnitude of the induced e.m.f. - State Faraday's Law of electromagnetic induction. - Account for Lenz's Law to predict the direction of an induced current and relate to the principle of conservation of energy. - Apply Faraday's Law of electromagnetic induction and Lenz's Law to solve problems. - Explain the production of eddy currents and identify their magnetic and heating effects. - Explain the need for laminated iron cores in electric motors, generators, and transformers. - Define Self Induction and its unit. - How is an inductor used to store electric potential energy? - Derive energy produced in Self Induction is E = 1/2 LI^2 - Explain Mutual Inductance (M) and its unit henry. - Describe the construction of a transformer and explain how it works. - Identify the relationship between the ratio of the number of turns in the primary and secondary coils and the ratio of primary to secondary voltages. - Recall that how step up and step-down transformers can be used to ensure efficient transfer of electricity along cables. - Describe the use of step-down and step-up transformers for the electric supply from power station to houses and electric appliances at home. - Solve problems using: NsVs / NpVp - Define motional emf and compute the potential difference across ends of a given rod or wire moving through a magnetic field. - Explain the construction and working of an AC generator. - Identify the factors affecting induced EMF of an AC generator. - Solve problems using: ξ =ξo Sin²πft - Describe the main features of an A.C motor and the role of each feature. - Explain the production of back emf in electric motors. ## Introduction Electromagnetic induction stands as a cornerstone in the realm of physics, serving as a fundamental principle that explains the dynamic relationship between electricity and magnetism. Discovered by the famous physicist Michael Faraday in the early 19th century, electromagnetic induction encompasses the phenomenon where the change in the magnetic fields induces the generation of an electromotive force (EMF) or voltage within a conductor. This revolutionary concept not only laid the groundwork for the understanding of essential electrical processes but also paved the way for the development of modern technologies such as electric generators and transformers. ## Production of Electricity by Magnetism In order to demonstrate that moving electric charges give rise to magnetic force, put a magnet compass near to current carrying wire the needle of compass will be deflected as shown in figure 19.1. This shows that moving charges produce magnetic field and in turn deflect magnetic compass. The working of electric motor is based on this simple phenomenon, the current carrying coil produce magnetic field which interacts with the surrounding magnets causing the coil to rotate. In this case the electric energy is being converted into mechanical energy. On the other hand, the moving magnet produces electric force. To observe this phenomenon connect a coil with a sensitive galvanometer and a magnet move inside it. The relative motion of coil and motion will produce induced electric current. If the motion of magnet is stopped induced current ceases to exist. ## Induced Electromotive force EMF Induced electromotive force (emf) can be generated in two primary ways: by *relative movement* and by *changing a magnetic field*. ### By Relative Movement (The Generator Effect) This method is based on *Faraday's Law of Electromagnetic Induction,* which states that an emf is induced in a conductor when it experiences a change in magnetic flux. The *generator effect*, also known as *motional emf*, occurs when there is a relative motion between a conductor and a magnetic field. ### By Changing a Magnetic Field (The Transformer Effect) This method also relies on Faraday's Law but involves changing the strength or orientation of a magnetic field around a stationary conductor. ## Faraday's Law of Electromagnetic Induction Faraday's Law of electromagnetic induction is a fundamental principle in electromagnetism that describes the relationship between a changing magnetic field and the *induced electromotive force (emf)* or voltage in a closed circuit. It can be stated as follows: The *electromotive force (emf)* induced in a closed circuit is *directly proportional to the rate of change of magnetic flux passing through the circuit*. Mathematically, Faraday's Law is often expressed as: - ε = -N ΔΦ / Δt ### Factors Affecting the Magnitude of the Induced EMF The magnitude of the induced electromotive force (emf) in a circuit or coil is governed by several factors, which are primarily described by Faraday's Law of electromagnetic induction. These factors include: - **Magnetic Flux Change:** If the rate of change of magnetic flux is higher, it will lead to a larger induced emf. Conversely, a slow change in the magnetic field will result in a smaller induced emf. - **Number of Turns in the Coil:** If a coil of wire has more turns, the greater will be the induced emf. Each turn of the coil contributes to the emf, so increasing the number of turns increases the overall emf. - **Area of the Coil:** The size of the coil or the area it encloses also affects the induced emf. A larger coil or a coil with a larger cross-sectional area will capture more magnetic flux lines, resulting in a larger induced emf. - **Angle between Magnetic Field and Coil:** The angle between the magnetic field lines and the plane of the coil affects the induced emf. When the magnetic field is perpendicular to the coil's plane (90°), the emf is maximized. When the field lines are parallel (0°), the emf is minimized. - **External Factors:** External factors such as temperature, material property, pressure, and other environmental conditions can also influence the induced emf, especially in situations where materials may exhibit nonlinear magnetic properties. ## Lenz's Law and Principle of Conservation of Energy After the introduction of Faraday's Law of electromagnetic induction, Heinrich Friedrich Lenz formulated a rule for determining the direction of an induced current within a loop. According to *Lenz's Law*: "The direction of induced emf in a circuit is always such that it opposes the cause which produces it." - *Lenz's Law and Conservation of Energy:* The principle of conservation of energy states that energy cannot be created or destroyed; it can only change forms. When we apply this principle to electromagnetic induction, we see that the work done in changing the magnetic field is converted into electrical energy in the form of the induced current. Hence Lenz's Law is in accordance with the law of conservation of energy. ## Eddy Currents Eddy currents are circulating currents induced in a conductor when it is exposed to a changing magnetic field. They are a common phenomenon in electromagnetic systems. These currents can have both magnetic and heating effects. ### Production of Eddy Currents Eddy currents are produced according to *Faraday's Law of electromagnetic induction*, which state that a changing magnetic field induces an electromotive force (emf) in a conductor. ### Magnetic Effects of Eddy Currents - **Counteracting Magnetic Field:** Eddy currents generate their own magnetic fields, and the direction of these fields opposes the original magnetic field that induced them. As a result, eddy currents create a magnetic field that counteracts the original magnetic field's change, thereby reducing the net magnetic field. - **Magnetic Damping:** In applications like electromagnetic brakes and magnetic dampers, eddy currents are intentionally induced to create a magnetic resistance that opposes motion. ### Heating Effects of Eddy Currents - **Joule Heating:** Eddy currents experience resistance as they flow through the conductor, and this resistance results in the conversion of electrical energy into heat, following *Joule's Law.* - **Reduction of Eddy Currents:** In many electrical systems, eddy currents represent an undesirable source of energy loss, especially in *transformers* and *electric motors*. To minimize these losses, laminated cores are used in transformers to break up the conducting paths and reduce the formation of eddy currents. ## Self-Induction When an electric current passes through a coil, it creates a magnetic field around it. If the current in the coil changes, either increasing or decreasing, the magnetic flux within the coil also changes accordingly. As a result of the change in magnetic flux, an induced emf is generated in the same coil. This process, where a changing current in the coil induces an emf in the coil itself, is *known as self-induction.* ### Unit of Inductance The unit of self-inductance is the *Henry (H)*, named after the American physicist Joseph Henry. One Henry (1 H) is defined as the amount of self-inductance in a circuit when a change in current of 1 ampere per second (1 A/s) induces an electromotive force (emf) of 1 volt (1 V) within the same circuit. ### Energy Stored in an Inductor An inductor is a passive electrical component that stores energy in the form of a magnetic field when an electric current flows through it. ### Mutual Inductance Imagine two closely positioned coils. The first coil, known as the primary coil, is connected to a battery through a variable resistor 'R' and a switch 'S.' The second coil, known as the secondary coil, is connected to a galvanometer. When the resistance is adjusted, it causes a change in the electric current 'I' within the primary coil. This change results in the production of a varying magnetic field that interacts with the nearby secondary coil. This phenomenon where a changing current in one coil induces an electromotive force (EMF) in another coil is *known as mutual induction*. ### Unit of Mutual Inductance One Henry (H) of mutual inductance can be defined as the mutual inductance between two coils when an EMF of one volt is induced in the secondary coil when the rate of change of current in the primary coil is one ampere per second. ## Transformers A transformer is an electrical device used to transfer electrical energy between two or more coils of wire through electromagnetic induction. It can either step up (increase) or step down (decrease) the voltage of an alternating current while keeping the frequency of the alternating current unchanged. It works on the principle of *mutual induction*. - **Construction of a Transformer:** Transformers consist of two coils of wire, known as the primary coil and the secondary coil, wound around a common magnetic core. The core is typically made of materials with high magnetic permeability, such as laminated iron or ferrite, to enhance the efficiency of the transformer. - **Working of a Transformer:** Imagine we have an alternating electromotive force (emf) applied to the primary coil. If, at a certain moment (t), the magnetic flux within the primary coil is changing at a rate of ΔΦ / Δt, this change in flux will induce a counteracting electromotive force (emf) in the primary coil, opposing the applied voltage. - **Step-Up or Step-Down Transformers:** The ratio of the number of turns in the primary coil (Np ) to the number of turns in the secondary coil (Ns) determines whether the transformer is a step-up or step-down transformer. If Ns > Np, then it's a step-up transformer and it increases the voltage. Conversely, if Np > Ns, then it is a step-down transformer and it decreases the voltage. - **Transmission of Electricity:** Step-down and step-up transformers are used for the electric supply from power station to houses and electric appliances. ## Motional EMF Motional electromotive force (emf) is a phenomenon that arises when a conductor moves through a magnetic field, inducing an electromotive force within the conductor. This concept is based on Faraday's Law of electromagnetic induction and is a fundamental aspect of electromagnetism. ## AC Generator An AC generator, also known as an alternator, is a device that converts mechanical energy into electrical energy in the form of alternating current (AC). It's based on the principle of electromagnetic induction, which was first described by Michael Faraday. - **Construction of an AC Generator:** An AC generator typically consists of the following four components: - Armature - Field magnet - Slip-rings - Brushes - **Working of an AC Generator:** The working of an AC generator involves several steps: - **Rotation of the Armature coil:** The coil or rotor is mechanically rotated using an external source of power, such as an engine, a turbine, or any other energy source. - **Generation of a Changing Magnetic Field:** As the rotor spins within the stator's magnetic field, the magnetic field within the rotor coil changes. This changing magnetic field induces an electromotive force (emf) or voltage in the coil. - **Generation of Alternating Current:** The induced voltage causes an electric current to flow through the coil, and since the magnetic field's direction is changing, the current produced is alternating in nature. - **Collection of Output:** The alternating current generated in the rotor coil is collected using slip rings and brushes. The brushes maintain contact with the slip rings as they rotate, allowing the generated AC to be drawn from the generator. ## AC Motor An AC (Alternating Current) motor is a device designed to convert electrical energy into mechanical energy by using alternating current. - **Components of an AC Motor:** The primary components as shown in figure and their roles in an AC motor are as follows: - **Stator:** The stator is the stationary part of the motor and contains the primary windings. - **Rotor:** The rotor is the rotating part of the motor. - **Bearings:** Bearings are essential components that support and allow the rotor to rotate within the stator. - **Shaft:** The shaft is connected to the rotor and extends beyond the motor housing. - **Cooling System:** Many AC motors incorporate cooling systems, such as fans or fins, to dissipate heat generated during operation. ## Back EMF In Electric Motors The concept of **back electromotive force (back EMF)** in electric motors is fundamental to understanding motor operation and efficiency. Back EMF is a self-generated electromotive force that opposes the applied voltage in a motor. It plays a crucial role in motor behavior, especially in limiting current and regulating speed. - **Electromagnetic Induction:** Back EMF is a consequence of Faraday's Law of electromagnetic induction, which states that a change in magnetic flux through a coil of wire induces an electromotive force (EMF) in that coil. In an electric motor, the coil of wire is typically part of the rotor or armature.