DHS 17 Electromagnetic Induction (Notes & Tutorial)

Dunman High School (Senior High Physics) 1 Topic 17 – Electromagnetic Induction Guiding Questions  If an electric current produces a magnetic field, can a magnetic field produce an electric current? What is required for this?  Can we achieve perpetual motion by invoking the magic of electromagnetism? Content  Magnetic flux  Laws of electromagnetic induction Learning Outcomes Candidates should be able to a. define magnetic flux as the product of an area and the component of the magnetic flux density perpendicular to that area b. recall and solve problems using  = BA c. define magnetic flux linkage d. infer from appropriate experiments on electromagnetic induction: i. that a changing magnetic flux can induce an e.m.f. ii. that the direction of the induced e.m.f. opposes the change producing it iii. the factors affecting the magnitude of the induced e.m.f. e. recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’s law f. explain simple applications of electromagnetic induction Introduction In the previous topic on Electromagnetism, we learned that when a current flows through a conductor in a magnetic field, it experiences a force. This phenomenon, governed by Fleming’s Left Hand Rule, can cause the conductor to move. But what if, instead of supplying a current, we apply a force to move the conductor through the magnetic field? Could this generate a current? The answer lies in the principle of Electromagnetic Induction, which forms the foundation of how electricity is generated in power plants and countless other systems. To understand this process, we must first explore the concept of magnetic flux and the fu ndamental laws of electromagnetic induction.

Dunman High School (Senior High Physics) 2 17.1 Magnetic Flux Magnetic field lines visually represent the strength and direction of a magnetic field. However, in certain situations, it is important to quantify how much of the magnetic field penetrates a given surface. This is where the concept of magnetic flux comes in. Magnetic flux measures the total number of magnetic field lines passing through a specific area A and helps us analyse the interaction between magnetic fields and surfaces. Magnetic Flux is defined as the product of an area and the component of the magnetic flux density perpendicular to that area. For a uniform magnetic flux density B at an angle θ to the normal of an area A, the magnetic flux Φ is given by cosB A BA    The SI unit of magnetic flux is the weber (symbol: Wb). 17.1.1 Magnetic Flux Linkage If the area A is bounded by a coil and the coil has N turns, then the total magnetic flux passing through the coil, also known as magnetic flux linkage through the coil, is cosN NBA  Magnetic Flux Linkage is the product of the magnetic flux passing through the coil and the number of turns on the coil. From the equation, magnetic flux linkage through a coil depends on a) the number of turns in the coil, N b) the magnitude of magnetic flux density, B c) the surface area of the coil, A d) the orientation of the coil , , with respect to the direction of B. (Note:  is the angle between the magnetic flux density and the normal to the surface of the coil,) A change in any of these variables results in a change of magnetic flux linkage. Area, A normal B θ

Dunman High School (Senior High Physics) 3 Example 1 The three loops of wire shown are all in a region of uniform magnetic field. Loop 1 swings back and forth as the bob on a pendulum, loop 2 rotates about a vertical axis and loop 3 oscillates vertically on the end of a spring. Which loop(s) have a magnetic flux that changes with time? Solution Example 2 A coil of 10 turns and area 0.35 m2 is placed perpendicular to a magnetic field of density 2.0 T as shown in the diagram on the left. Points P and Q are pulled apart until the coil becomes a straight line as shown in the diagram on the right. What is the change in magnetic flux linkage through the coil? Solution Region of magnetic field Before After P Q P Q

Dunman High School (Senior High Physics) 4 17.2 Electromagnetic Induction Ten years after the discovery that an electric current could produce a magnetic field, independent experiments conducted independently by Joseph Henry in United States and Michael Faraday in England showed that a changing magnetic field could induce an electric current in a circuit. The results of these experiments led to the formulation of a basic and important law known as Faraday’s law. 17.2.1 Faraday’s Law Faraday’s Law of electromagnetic i nduction states that the magnitude of the induced e.m.f. is directly proportional to the rate of change of the magnetic flux linkage. Mathematically: ( ) ( cos )d N d NBA dt dt     e.m.f. induced depends on quantities such as N number of coils, magnetic flux density B, area of coil A and angle  between B and normal of A. 17.2.2 Lenz’s Law Lenz’s Law states that the induced current is in a direction so as to produce effects which oppose the change in magnetic flux. Lenz’s law is not written separately but combined with Faraday’s law to form an equation. ( cos )d NBA dt   The negative sign represents direction of induced current is always such the magnetic field due to the current opposes the change in the magnetic flux that induces the current. Furthermore, the direction of an induced e.m.f. is that of the induced current. The key word in Lenz’s law is “opposition.” Note: A current is induced only if there is a complete circuit. An e.m.f. is always induced when there is a change in magnetic flux linkage.

Dunman High School (Senior High Physics) 5 Example 3 A circular coil of diameter 2.0 cm has 3000 turns. It is rotated in a magnetic field of flux density 1.8 T from position X to position Y in 0.060 s. What is the average e.m.f. induced in the coil during the rotation? A 28 V B 36 V C 113 V D 1800 V Example 4 The diagram shows a magnet placed close to a flat circular coil. a) Explain why there is no induced e.m.f. even though there is magnetic flux linking the coil. There is no change to the magnetic flux linking the coil, hence according to Faraday’s law, there is no induced e.m.f. b) Explain why there is an induced e.m.f. when the magnet is pushed towards the coil. The magnetic flux density B increases as the magnet moves towards the coil. [1] There is an increase in the magnetic flux linking the coil, hence an e.m.f. is induced across the ends of the coil. [1] c) Indicate direction of current in the coil by drawing arrows on the coil. d) What if coil was pushed away from magnet? This part is out of the plane (towards the viewer).

Dunman High School (Senior High Physics) 6 Example 5 Predict the direction of the induced current in the circular coil for each of the following cases: Action Direction of induced current Pulling the coil to the right out of a magnetic field pointing out of the plane of the page. Shrinking a coil in a magnetic field pointing into the plane of the page. Rotating the coil by pulling the left side towards us and pushing the right side in with the magnetic field pointing right to left. Increasing the current in a wire that is placed below a coil in the plane of the page.

Dunman High School (Senior High Physics) 7 Example 6 A rod of length 0.20 m moves at a steady speed of 3.0 m s −1 at right angles to a magnetic field of flux density 0.10 T. (a) Use Faraday’s law to determine the e.m.f. induced across the ends of the wire. Also determin