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CHAPTER TWO ELECTROMAGNETIC INDUCTION 1|P a g e (1) ELECTRIC, MAGNETIC AND LORENTZ FORCES Q) What happens when a charged particle is thrown into an electric field? Why? If a positively charged particle (+q) moves in a perpendicular direction to the lines of a unifo...

CHAPTER TWO ELECTROMAGNETIC INDUCTION 1|P a g e (1) ELECTRIC, MAGNETIC AND LORENTZ FORCES Q) What happens when a charged particle is thrown into an electric field? Why? If a positively charged particle (+q) moves in a perpendicular direction to the lines of a uniform electric field (E), this particle will be affected by electric force (FE) parallel to lines of electric field, which illustrates electric force which given by the following relation: 𝑭 𝑬 = 𝒒𝑬 Where FE: electric force. E: electric field. q: charge. Q) What happens when a charged particle is thrown into a uniform magnetic field and in a perpendicular direction to it? Why? If the particle moves with a velocity (𝜈⃑) perpendicularly on the lines of a uniform magnetic field, with a flux density (B). It will be affected by a magnetic force (FB) is perpendicular on that flux, the particle will deviate from its original path, it will follow a circular path because the magnetic force affects perpendicularly on the velocity vector (𝜈⃑). The vector formula for magnetic force is given by the following relation: Where FB: magnetic force. v: particle velocity. q: charge. B: magnetic flux density. 2|P a g e  Q) Write the vector formula for the magnetic force, and the mathematical formula for calculating the amount of the magnetic force. Directional (vector) formula for magnetic force: Mathematical formula for calculating the amount of magnetic force: Q) How to determine the direction of the magnetic force affecting a charge entering a uniform magnetic field? By “the right hand rule”, where the right-hand fingers rotate in the direction of velocity (V) towards the magnetic field (B), so, the thumb indicates the direction of the force (FB) in the case that the charge is positive. 3|P a g e  Q) When the magnetic force is: 1) Equal to the maximum. 2) Equal to zero. 1) The maximum value is if the velocity vector (V) is perpendicular to the flux vector (B) and the angle is: 𝜽 = 𝟗𝟎° ∴ 𝑭𝑩 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝟗𝟎 𝑭𝑩 = 𝒒𝒗𝑩 (𝟏) 𝑭𝑩 = 𝒒𝒗𝑩 2) The zero value is if the velocity vector (V) is parallel to the flux vector (B) and the angle is: 𝜽 = 𝟎 ∴ 𝑭𝑩 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝟎 𝑭𝑩 = 𝒒𝒗𝑩 (𝟎) 𝑭𝑩 = 𝟎 Q) What is the Lorentz force? In what field it may use? It is the resultant of the electric and magnetic forces acting on an electric charge entering perpendicularly in the two fields: Lorentz force is used in practical applications, like Cathode –ray tube that controls the path electronic band on the monitor, Ministerial Exams: Q.1) What is happening and why? If a positively charged particle (+q) moves in a perpendicular direction to the lines of a uniform magnetic field with a flux density (B)? 4|P a g e Q.2) What is happening and why? If a positively charged particle (+q), when moves with a velocity of (V) in a perpendicular direction to the lines of an electric field? Q.3) Explain how you can practically know whether a magnetic field or an electric field is present in a certain space? Q.4) What is the Lorentz force? In what field it may use? (2) ELECTROMAGNETIC INDUCTION Q) Who is the scientist who is considered the first to create the relationship between electric and magnetic? What is his discovery? The Scientist Oersted He discovered that the electric current flowing into a conductor generates a magnetic field, and the amount of the magnetic field depends on the amount of electric current. Q) Explain, how does an electric current generate in the coil to which the ammeter is connected in the following cases? 1- If the magnetic rod is at rest relative to the coil. 2- If we hold the magnetic rod by hand and direct its north pole to one sides of the coil 3- If the magnetic rod removed from the hollow of the coil and its north pole facing it. 1) When the magnetic rod is at rest relative to the coil, the reading of the ammeter is zero. Because the magnetic flux (Ø) , which penetrates the coil, does not change through time. Moreover, there is no relative motion between the magnet and the coil. Therefore, no current pass through the circuit. 2) when we hold the magnetic rod by hand and direct its north pole to one sides of the coil, push it towards the coil and a parallel to coil axis, we find the ammeter indicates deflection of current in the circuit in a certain direction. The reason for this is increase in magnetic flux (Ø), which penetrates the coil when the magnet approaches to the coil. 3) When the north pole of the magnet moves away, facing the core of the coil, and parallel to its axis, the ammeter will indicate a current flowing in a direction opposite to the approach. This is due to a decrease in the amount of magnetic flux (Ø) penetrating the coil. 5|P a g e  Q) What does the induced current flowing into the coil depends on? Q) What are the factors affecting the induced current? 1) Velocity of relative motion between the magnet pole and the coil. 2) Number of turns for the coil. 3) The amount of magnetic flux penetrates the coil. 4) Magnetic Permeability of Core coil Material. Q) What is Faraday's conclusion? Or What is the phenomenon of electromagnetic induction? An induced current is generated in a closed circuit (like a wire coil or conductive ring) only ∆∅ when there is change in the magnetic flux which penetrates that circuit per unit time ( ). ∆$ Q) Why did the attempts that preceded Faraday's discovery failed to generate an electric current with a magnetic field? This is because all attempts relied on static magnetic fields only. Q) What is the requirement to have an induced current? That the circuit be closed... and that a change occurs in the magnetic flux that penetrates the circuit in the time unit. Q) What is the condition for obtaining an induced electro-motive force? the change in the magnetic flux that penetrates the coil to the unit time Q) What is the condition for obtaining an induced electric motive force and an induced current? That the circuit be closed... and that a change occurs in the magnetic flux that penetrates the circuit in the time unit. 6|P a g e  Q) Explain an experiment illustrating the discovery and deduction of the scientist Faraday? two coils of two wires wrapped around a closed ring of wrought iron. One of the coils is connected in series combination to a battery and a switch the circuit on the left side, which is called the primary coil circuit, while the other coil is connected to a device that detects small currents. It has zero point in the middle (circuit on the right side) this one is called the secondary coil circuit. Faraday observed deflection of the pointer, connected to the secondary coil, to one of the sides at the switch connected to the primary coil is turned off, then it goes back to zero, coil circuit, this current is called "induced current", although there is no battery or voltage source in this circuit. As for the pointer goes back to zero after closing the switch, it was because the current flow in the primary coil circuit was constant. Hence, there was no change in the magnetic flux, which penetrated the ∆∅ secondary coil per unit time ( ) ∆$ Faraday also noticed that another deflection in the pointer of the gauge again, at the moment when the switch is opened, but this time the deflection was opposite to zero, then it went back to zero. Faraday’s observation was this effect (current flow in the secondary circuit) accrued only during the two stages of growth and decay of current in the primary coil circuit. Since both growth and decay of current in the primary coil circuit would cause increase and decrease in the magnetic flux, that penetrates the core of iron that wrapped in the two coils. 7|P a g e Therefore, Faraday pays attention to the necessity of the availability of the basic factor to generate induced current in a closed circuit, the change in the magnetic flux that penetrates the coil to the unit time. According to this, Faraday concluded: An induced current is generated in a closed circuit (like a wire coil or conductive ring) only ∆∅ when there is change in the magnetic flux which penetrates that circuit per unit time ( ) ∆$ Q) Explain an activity (experiment) that demonstrates the electromagnetic induction phenomenon? Activity Tools: Two hollow coils of different diameters (one can be inserted in the other). Galvanometer with zero reading in the middle Magnetic rod. wires. Battery. Electric switch. Activity Steps: (First): One end of the coils is connected to the galvanometer. Put north end of the magnetic rod faces the coil during in activity for the coil. We will find that galvanometer pointer will remain fixed at zero scale. There is no flow of current in the coil circuit. The magnetic rod is pushed towards the coil, then moved away. We find that the galvanometer pointer deflects to one side of zero scale (when the rod is close) and the pointer moves to the opposite direction (when is moved away). This indicates induced current flow in the coil, in both cases. (Second): Connect the two ends of other coil (primary coil) are connected to a battery terminal by wires to create electromagnet. The primary coil connected to the battery is moved in front of the secondary coil which connected to the galvanometer, brought it closer and then moved away from it which is parallel to its axis. What do you notice? 8|P a g e  We note that the pointer of galvanometer is deflected on one side about zero scale and in opposite direction again. This indicates an induced current flow in the secondary coil circuit and then it goes back to zero when there is no relative motion between the two coils. (Third): Connect an electrical switch to the primary coil circuit and make it open. Insert the primary coil is in the secondary coil; the ratio of both is maintained. Will the galvanometer pointer deflect? Close and open the switch in the primary coil circuit. What do you notice? We find the galvanometer pointer deflects by moving on both sides of the zero reading in opposite directions only once the switch is turned on and off in the primary coil circuit respectively. It indicates flow of induced current in the secondary coil circuit in those two ways Conclusion: An electromotive force is induced (ɛind) and an induced current (Iind) flows in a closed circuit (conductive ring or a coil) only when there is change in the magnetic flux that penetrates that circuit per unit time, (although there is no battery in that circuit). The polarity of the induced emf (ɛind) and direction of the induced current (Iind) in the electric circuit, have a certain direction when there is increase in the magnetic flux that penetrates it, and they have opposite direction when the flux decreases. Ministerial Exams: Q) Explain an activity (experiment) that demonstrates the electromagnetic induction phenomenon? (3) MOTIONAL EΜF (𝜺𝒎𝒐𝒕𝒊𝒐𝒏𝒂𝒍 ) Q) What is the motional electromotive force? It is an electric potential difference is generated between ends of the rod by moving a conductor rod in a uniform magnetic field. It is considered as a special case of electromagnetic induction 9|P a g e  Q) Derive the mathematical formula for the motional electromotive force? 𝑭𝑬 = 𝑭𝑩𝟏 𝒒𝑬 = 𝒒𝒗𝑩 𝑬 = 𝒗𝑩 ∆𝑽 ∵𝑬= 𝒍 ∆𝑽 ∴ = 𝒗𝑩 𝒍 ∆𝑽 = 𝒗𝑩𝒍 ∴ 𝜺𝒎𝒐𝒕 = 𝒗𝑩𝒍 Where Emot: motional electromotive force. v: rod velocity. l: rod length. B: flux density. Q) What are the factors, the motional electromotive force depends on? 1) velocity of the rod. (v). 2) density of magnetic flux (B). 3) length of the rod (l). 4) the situation of the rod with respect to the magnetic flux. (The angle between the velocity vector and the magnetic flux density vector). 𝜺𝒎𝒐𝒕 = 𝒗𝑩𝒍 𝒔𝒊𝒏𝜽 10 | P a g e  Q) When the conductor rod moves inside a magnetic flux, the positive charges collect at one end of the rod and the negative charges at the other end, generating (𝜺𝒎𝒐𝒕 ), give a reasons for this? Inducing emf by moving a conductor rod inside a uniform magnetic field, As a result of, the movement of the conductor rod inside the magnetic field, the positive charges of the rod are affected by a magnetic force 𝑭𝑩𝟏 = 𝒒𝒗𝑩 𝒔𝒊𝒏𝜽 When the rod is moved perpendicularly against the magnetic flux, this force is expressed as follows: 𝑭𝑩𝟏 = 𝒒𝒗𝑩 According to the “right-hand rule”, this force works to separate the positive charges on one side and the negative charges on the other side. Charges continue to collect at both ends of the rod, and an electric potential difference called (motional electromotive force) is generated. If the direction of the moving rod is reversed or the magnetic field is reversed, will the polarity of the motional electromotive force ( 𝜺 motional) reverse? Yes... the polarity of the motional electromotive force is reversed. Q) What is the origin of the force impeding to the movement of the conductor rod in a magnetic field? Due to the flow of an induced current in the rod in a perpendicular direction to the magnetic flux, a magnetic force appears affecting this rod, given by the following equation: 𝑭𝑩𝟐 = 𝑰𝑩𝒍 By applying the right-hand rule, we find that the force acts in a perpendicular direction to the rod and is opposite to the direction of the velocity (v) with which the rod moves. And it moves toward the left side. Therefore, this force obstructs the movement of the rod. 11 | P a g e  Q) Is there an induced current flow in the circuit figure? If yes, determine the direction of induced current in it. The induced current does not flow because the velocity direction is parallel to the direction of the flux density and then the angle between (B & v) are equals zero (θ = 0) and from the equation: 𝑭𝑩 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝜽 𝜽 = 𝟎 𝑭𝑩 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝟎 𝑭𝑩 = 𝒒𝒗𝑩 (𝟎) 𝑭𝑩 = 𝟎 Q) Mathematically prove that electromagnetic induction obeys the law of conservation of energy. 12 | P a g e  Q) Derive the mathematical equation for the external pull force (Fpull) affecting a conductor in which an induced current pass, moves in a uniform magnetic field and is perpendicular to it. Ministerial Exams: Q.1) What is the motional electromotive force acting on both ends of a conductor rod (which moving according to a uniform magnetic field) depends on? Q.2) What does the kinetic electromotive force acting on both ends of a conducting rod is moving relative to a uniform magnetic field, depends on? (4) MAGNETIC FLUX AND FARADAY'S LAW Q) What are the methods for obtaining a change in the magnetic flux (∅) when there is a relative movement between the magnet and the coil? According to the equation: ∅ = 𝑨𝑩 𝒄𝒐𝒔𝜽 1) Change in angle measurement (θ) between area vector (A) and magnetic flux density vector ( B ). is changed by rotating the ring or coil inside a uniform magnetic field. 13 | P a g e 2) Changing area of the ring facing the uniform magnetic flux (Φ). This is done by pressing the ring or pulling it from opposite sides, thus area (A) reduces. 3) Moving the conductive ring in a plane perpendicular to a uniform magnetic flux: (Pushing the ring to be inserted into a uniform magnetic field or pulling it out of the field). 14 | P a g e  Q) Write the equation for the magnetic flux, and explain when it be with the maximum amount and when it be with the minimum amount? ∅ = 𝑨𝑩 𝒄𝒐𝒔𝜽 Where: (∅): is the angle between a vector (B) and a vector (A). (B): The density of the magnetic field. (A): The area of the ring. The flux be with the maximum amount when the (B) vector be in parallel with (A) vector, as (θ = 0), that: ∅ = 𝑨𝑩 𝒄𝒐𝒔𝟎 = 𝑨𝑩 The flux be with the minimum amount when the (B) vector be in perpendicular direction to the (A) vector, as (θ = 90), that: ∅ = 𝑨𝑩 𝒄𝒐𝒔𝟗𝟎 = 𝟎 Q) What is the measure unit of: 1) Magnetic flux? 2) The time rate of change of the magnetic flux? 3) Magnetic flux density? 1) The magnetic flux (∅) is measured in units of Weber (web). ∆∅ %& 2) The time rate of change of the magnetic flux ( ) is measured in units ( ). ∆$ '&( %& 3) The magnetic field density (B) is measured in units of Tesla (T) and Tesla is equal to ( ! ). ) 𝒘𝒃 Q) Prove that Tesla is equal to ( )? 𝒎𝟐 ∅ = 𝑨𝑩 𝒄𝒐𝒔𝜽 ∴ 𝒘𝒃 = 𝒎𝟐 ∙ 𝑻 𝒘𝒃 𝑻= 𝒎𝟐 15 | P a g e  Q) What is the text of Faraday's law? With mention of the mathematical equation? Amount of induced electro motive force (𝜀-./ ) in a conductive ring is directly proportional to the time rate of change in the magnetic flux that penetrates the ring Faraday's law mathematical equation: ∆∅ 𝜺𝒊𝒏𝒅 = −𝑵 ∆𝒕 Q) What is the (𝜺𝒊𝒏𝒅 ) polarity depends on? It depends on the magnetic flux whether it is increasing or decreasing. Q) What causes an electrical current to flow in a closed circuit? The presence of a source of electric motive force (𝑉011 ) such as a battery or generator. Q) What causes an induced current to flow in a closed circuit? The presence of an induced electromotive force (𝜀234 ), which is generated by a change in magnetic flux in the unit of time. Ministerial Exams: Q.1) What is required in a closed circuit to generate: a) An electric current. b) An induced current. Q.2) What are the physical quantities that are measured in the unit of (𝐰𝐞𝐛𝐞𝐫/𝐦𝟐 )? 16 | P a g e