Untitled Flashcards Set

Module 6: Electromagnetism 1 Module 6: Electromagnetism Charged Particles, Conductors and Electric and Magnetic Fields 📖 investigate and quantitatively derive and analyse the interaction between charged particles and uniform electric fields, including: – electric field between parallel charged plates 𝐸=𝑉𝑑 ✅ – acceleration of charged particles by the electric field ⃗net=𝑚⃗,⃗=𝑞⃗⃗ ✅ – work done on the charge 𝑊=𝑞𝑉,𝑊=𝑞𝐸𝑑,𝐾=12𝑚𝑣2 ✅ The Electric Field Electric fields are created by charged objects and exert forces on other charged objects. Charge is a fundamental property of matter. Electric field is a vector quantity and the force per unit charge at a point. Therefore its units are N/C or V/m. A uniform electric field has a constant magnitude and direciton. Electric field lines can be used to represent electric fields. The direction of the field line indicates the direction of the force a positiove charge would experience if placed in the electric field. The density of the field lines is proportional to the field strength. Parallel Charged Plates To produce a strong, uniform electric field two parallel plates with opposite charges can be used. The field is unifirm between the plates but becomes nonuniform very close to the ed Module 6: Electromagnetism 2 There is a potential difference present between the plates. Potential difference is the change in electrical potential between the two plates. Electric potential is the electric potential energy, potential energy possessed, per unit charge, measured in volts, V. The potential where: E = electric field (V/m) ΔV = potential difference (V) d = distance between plates (m) Acceleration Of Charged Particles By An Electric Field The electric field is defined as the electrostatic force per unit charge exerted on a small positive test charge. The electrostatic force is the force exerted by an electric field. where: F = electrostatic force (N) q = charge (C) E = electric field (N/C) Note that the acceleration of an object due to force is give by Newton's second law. E = d ΔV F = qE F = ma Module 6: Electromagnetism 3 where: F = force (N) m = mass (kg) a = acceleration (m/ ) These two equation can be combined since F = qE = ma to give an expression to find the acceleration of a charged particle by an electric field. where: a = acceleration (m/ ) q = charge (C) E = electric field (N/C) m = mass (kg) When the charge is positive, a and E will have the same direction but when the charge is negative, a and E will have different directions. Work Done In A Uniform Electric Field Electric potential energy is a form of potential energy stored in an electric field. Work is done on a field when a charged particle is forced to move in the electric field. Conversly, when energy is stored in the electric field then work is done by the field in the particle. Electric potential is defined as the work required per unit charge to move a positive charge from infinity to a place in the electric field. Electric potential at infinity is defined as zero. where: W = work done (J) q = charge (C) V = electric potential (V or J/C) This equation can be combined with other to produce: s 2 a = m qE s 2 W = qV Module 6: Electromagnetism 4 where: W = work done (J) q = charge (C) E = electric field (V/m or N/C) d = distance (m) Work can be done by the electric field on a charged object or on the electric field by forcing the object to move. If a charged object i smoving in the direction it would naturally tend to go within the electric field, then work is being done by the field. When work is done by a charged object on an electric field, the object is forced to move against the direction it would naturally go. Work has been done on the field by forcing the object against the field. If a charge doesn't move any distance parallel to the direction of the field then no work has been done on or by the field. 📖 model qualitatively and quantitatively the trajectories of charged particles in electric fields and compare them with the trajectories of projectiles in a gravitational field ✅ Gravitational & Electric Fields Gravitational Fields are very similar to electric fields. The gravitational field is created by, and acts on, objects with mass. The gravitational force is in the direction of the field. The electric field is created by, and acts on, objects with charge. The electric force is in the direction of, or opposite the direction of, the field. W = qEd Module 6: Electromagnetism 5 Trajectory Of Charged Particle In Uniform Electric Fields In a uniform electric field, the trajectory of a charged particle is a projectile trajectory. The particle experiences a constant force parallel to the field, and hence a constant acceleration, parallel to the field. Perpedicular to the field the acceleration is zero, so velocity is constant. A charged particle may accelerate in the direction of the electric field, or in the opposite direction. For a positive charged particle, the force is in the direction of the field; for a negative charged particle the force is in the direction opposite to the field. Module 6: Electromagnetism 6 📖 analyse the interaction between charged particles and uniform magnetic fields, including: – acceleration, perpendicular to the field, of charged particles ✅ – the force on the charge 𝐹=𝑞𝑣⊥𝐵=𝑞𝑣𝐵sin𝜃 ✅ Charged Particles In Magnetic Fields Electric fields are created by charged particles. Magnetic fields are created by moving charged particles (current). This magnetics field can interact with other externa magnetic fields resulting in forces. Hence, a moving charge will experience a fore when placed in an external magnetic field. A stationary charged particle experiences a force due to electric field, but not a constant magnetic field since the charge has to be moving relative relative to the magnetic field. This force experiences by the charged particle is called the Lorentz force. The magnitude of the Lorentz force is propertional to its charge, strength of external magnetic field and speed of particle. The particle experiences a maximum force when it moves perpendicular to the field and a zero force if it moves parallel to the field. where: F = lorentz force (N) q = charge (C) v = velocity (m/s) F = qvB sin θ Module 6: Electromagnetism 7 B = magnetic field (T) = angle between velocity vector and magnetic field ( ) The direction of the Lorentz force will always be perpendicular to the magnetic field. To find the direction of the Lorentz force, the right hand palm rule is required. Right Hand Palm Rule The right hand plam rule can be used to determine the direction of the Lorentz force. To perform the right hand palm rule, point the thumb in the direction of motion of positive charge. Then point your fingers in the direction of the external magnetic field lines. The palm pushed in the direction of the Lorentz force. Path Of A Charged Particle In A Uniform Magnetic Field When a charged particle is moved in a uniform magnetic field it will experience a force called the Lorentz force casuing the particle divert from its original path. As the direction of the charged particle changes, so does the angle of the force acting in it. This will cause the charged particle to move in a circular motion in the magnetic field. θ ° Module 6: Electromagnetism 8 The radius of the orbit of the charged particle is given by: where: r = radius (m) m = mass (kg) v = velocity (m/s) q = charge (C) B = magnetic field (T) The orbital period of the charged particle is given by: where: T = orbital period (s) m = mass (kg) q = charge (C) B = magnetic field (T) Another possible path of a charged particle in a magnetic field is a helix. This occurs if the particle has a velocity component in the direction of the field r = qB mv T = qB 2πm Module 6: Electromagnetism 9 (velocity is at an angle to field between 0 and 90 degrees). The parallel component of the velocity is not altered by the field. Synchrotron A synchrotron is a particle acceleration where electrons are accelerated around a huge ring to almost the speed of light with high energies. These charges are forced to move in circular paths due to magnetic fields generated by bending magnets. When accelerating, electrons give off bursts of radiation which is channelled down tubes called beamlines and used by researchers for experiments. Work Done On A Charged Particle In Uniform Magnetic Field No work is done by the net centripetal force on an object in circular motion since force and velocity are always perpendicular. Hence, magnetic field does no work on a charge in circular motion. Since acceleration is always perpendicular to the path, and speed is constant, then kinetic energy is also constant. For any path that a charged particle takes in a uniform magnetic field, the force is always perpendicular to the velocity and no work is done. 📖 compare the interaction of charged particles moving in magnetic fields to: – the interaction of charged particles with electric fields ✅ – other examples of uniform circular motion ✅ Gravitational, Electric And Magnetic Fields Module 6: Electromagnetism 10 Gravitational, electric and magnetic field are all defined as fields = force / property, where property is the thing that creates the field and in which the field acts on. The electrostatic force acts on a charged particle and the gravitational force acts on a particle with mass. But the magnetic force acts on a charge particle in motion. The gravitational and electric force vectors are parallel to the direction of the field, but the magnetic force vector is perpendicular to the magnetic field. Force due to gravity is always in the direction of the field, but the force due to electric field can be either in the direction of a field line or opposite to it. The path of a charged particle in an electric field or a mass in a gravitation field is that of a projectile. While when a charged particle moves perpendicular to a uniform magnetic field it diverts into a circular path. If the charged particle has components both parallel and perpendicular to the field then it undergoes a helical path. gravitational and electric forces can do work in displacing a charge particle but the magnetic force does no work since force is perpendicular to the displacement. The Motor Effect 📖 investigate qualitatively and quantitatively the interaction between a current-carrying conductor and a uniform magnetic field 𝐹=𝑙𝐼⊥𝐵=𝑙𝐼𝐵sin𝜃 to establish: – conditions under which the maximum force is produced ✅ – the relationship between the directions of the force, magnetic field strength and current ✅ – conditions under which no force is produced on the conductor ✅ The Motor Effect The motor effect is a phenomenon that occurs when a conducting wire is exposed to an external magnetic field. Since a conducting wire is essentially a flow of charged particles, it will experiences a force exerted by the magnetic Module 6: Electromagnetism 11 field. The motor effect is used to convert electric potential energy into kinetic energy. The force extered on the conductor is proportional to the strength of the magnetic field, the current and length of wire exposed to the magnetic field. where: F = force (N) B = magnetic field (T) I = current (A) = length of wire exposed to magnetic field (m) = angle between wire and magnetic field ( ) To find the direction of the force actingon the conducter by the field can be found using the right hand palm rule. The force on the conductor is at a maximum when the conductor is at right angles to the field. The force is zero when the conductor is parallel to the magnetic field. 📖 conduct a quantitative investigation to demonstrate the interaction between two parallel current-carrying wires ✅ analyse the interaction between two parallel current-carrying wires 𝐹𝑙=𝜇02𝜋𝐼1𝐼2𝑟 and determine the relationship between the International System of Units (SI) definition of an ampere and Newton’s Third Law of Motion ✅ Forces Between Conductors F = BIℓ sin θ ℓ θ ° Module 6: Electromagnetism 12 A conductor carrying a current will produce a magnetic field surrounding it since there is a flow of charge. Assume two current carrying wires adjacent to one another. The two conductors are going to exert an equal force on one another. where: = force per unit length between conductors (N/m) = magnetic permeability of free space (4π x N/ ) = current in conductor 1 (A) = current in conductor 2 (A) r = distance between conductors (m) Notice both forces exerted by each conductor is equal. This is because of Newton's thrird law: when one body exerts a force on another body, the second body exerts an equal force in the opposite direction onto the first body. If two parallel conductors carry current in the same direction, the forces attract. If the two parallel conductors carry current in the opposite direction then the forces repel. This can be proven using the right hand rule. The Amphere The base unit for measuring electric current in the International System Of Units (SI) is the amphere (A). The amphere is defined as being equal to the amount of current needed through two identical parallel conductors of infinite length when = ℓ F 2πr µ0I1 I2 ℓ F µ0 10−7 A2 I1 I2 Module 6: Electromagnetism 13 they are 1 meter apart, in order to produce a fore per unit length of 2 x 10^-7 N/m. Electromagnetic Induction 📖 describe how magnetic flux can change, with reference to the relationship 𝛷=𝐵∥𝐴=𝐵𝐴cosθ. ✅ Electromagnetic Induction Electromagnetic induction is the production of an electric current due to a change in the magnetic field acting on the conductor. Magnetic Flux Magnetic flux is a measure of the amount of magnetic field that passes through an area. It can also be a measure of how many field lines pass through an area. This is why magnetic field strength can be refered to as magnetic flux density. A strong magnetic field acting over small area can produce equal magnetic flux as a weaker magnetic field acting over large area. Module 6: Electromagnetism 14 The area vector (A) is the normaal to the plane of the area. where: 𝛷 = magnetic flux (Wb) B = magnetic field strength (T) A = area ( ) = angle between magnetic field and area vector ( ) The magnetic flux will be at maximum when the area vector is parallel to the magnetic field and zero when the area vector is perpendicular to the magnetic field. ϕ = BAcosθ m2 θ ° Module 6: Electromagnetism 15 Changing Magnetic Flux Magnetic flux can vary if their is a change in magnetic field strength, area vector or angle between area vector and magnetic field. Flux is a scalar quantity and can either be positive or negative. If a flux is positive and increases, then change in flux is positive. Conversely, if flux decreases then change in flux is negative. 📖 analyse qualitatively and quantitatively, with reference to energy transfers and transformations, examples of Faraday’s Law and Lenz’s Law 𝜀= −𝑁𝛥𝛷𝛥𝑡, including but not limited to: – the generation of an electromotive force (emf) and evidence for Lenz’s Law produced by the relative movement between a magnet, straight conductors, metal plates and solenoids ✅ – the generation of an emf produced by the relative movement or changes in current in one solenoid in the vicinity of another solenoid ✅ Faraday's Law Of Induction Faraday's law of induction states the average emf induced in a conducting loop exposed to a changing magnetic flux is proportional to the rate of change of flux. where: = average emf induced (V) N = number of loops = change in flux = change in time The negative sign is present for the direction of the induced emf. Lenz's Law Lenz's law states that an induced emf always produces a current whose magnetic field will oppose the initial change in flux. Lenz's law obeys the ε = −N Δt Δϕ ε Δϕ Δt Module 6: Electromagnetism 16 principle of conservation of energy and determined direction of induced emf. To determine direction of current 3 steps must be followed: 1. What is the change that is happening 2. What will oppose the change and/or restore the original conditions 3. What must be the current direction to match this opposition The right hand grip rule is used for step 3. Wrap your fingers around the coil so the fingers point in the direction of the oppositional magnetic field and the direction of the thumb indicated the induced current. Inducing Current A magnetic flux change can be created by any method that causes a relative change in strength of the magnetic field. An can be emf induced in 3 ways: changing magnetic field strength changing area of coil Module 6: Electromagnetism 17 changing orientation of coil with respect to the magnetic field Eddy's Current When a metal plate is exposed to a changing magnetic field by Faraday’s law it will cause a current to be induced in the metal. The currents are named eddy currents and travel in a circle. By Lenz’s law these currents will be in such direction that they create a magnetic field that opposes the initial change in flux and apply a force that opposes its source of motion. A situation where eddy currents are involved is when a magnetic material is falling through a non magnetic metal tube. As the magnet fall through, this produces a changing magnetic flux in walls of both tubes. By Lenz's law, this will induce a current in the tube called eddy current that will produce their own magnetic field to try and oppose the initial change in flux and also the motion of the magnet. Resulting in an opposing force on the falling magnet that cause is to slow down. 📖 analyse quantitatively the operation of ideal transformers through the application of: – 𝑉p𝑉s=𝑁p𝑁s ✅ – 𝑉p𝐼p=𝑉s𝐼s ✅ Transformers Module 6: Electromagnetism 18 A transformer increases (step up) or decreases (step down) an AC voltage using the principle of a changing magnetic flux. AC current in primary coil generates a changing flux that is directed to secondary coil where changing flux induces an emf in the coil. In an ideal transformer no energy is lost. AC voltage in primary and secondary coil will be of the same frequency. A transformer relies on the principle of a changing magnetic flux. If a DC current is running through a transformer, since it doesn’t alternate and flow in the other direction their will be not change significant change in flux. Meaning no magnetic flux will be directed through the secondary coil and not current will be induced. The Transformer Equation where: = emf in primary coil (V) = emf in secondary coil (V) = number of primary coils = number of secondary coils Power Output In an ideal transformer no energy is lost. Hence power in the primary coil is equal to the power in the secondary coil where: = current in secondary coil (A) = VS VP NS NP VP VS NP NS = IP IS NS NP IS Module 6: Electromagnetism 19 = current in primary coil (A) = number of primary coils = number of secondary coils 📖 evaluate qualitatively the limitations of the ideal transformer model and the strategies used to improve transformer efficiency, including but not limited to: – incomplete flux linkage ✅ – resistive heat production and eddy currents ✅ Resistive Heat Production & Eddy Currents Eddy currents can be produced in the core causing heating. To prevent this, the magnetic core materials that have low electrical conductivity is chosen. Also, the use of thin metal sheet called laminations is present since electrons cannot across the insulating gap between laminations and so are unable to circulate on wide arcs. Laminated magnetic cores are made of stacks of thin iron sheets coated with an insulating layer 📖 analyse applications of step-up and step-down transformers, including but not limited to: – the distribution of energy using high-voltage transmission lines ✅ Effectiveness Of Transformers Transformers are useful because not as much power is lost. This is because when the voltage is stepped up the current will reduce as P =VI. Since then if the current is reduced by a factor of x and the resistance stays constant then the power loss will reduce by a factor of . The lower the current, the lower the resistance losses in the conductors. And when resistance losses are low, energy losses are low also. IP NP NS PLoss = I 2R x 2 Module 6: Electromagnetism 20 Applications of the Motor Effect 📖 investigate the operation of a simple DC motor to analyse: – the functions of its components ✅ – production of a torque 𝜏=𝑛𝐼𝐴⊥𝐵=𝑛𝐼𝐴𝐵sin𝜃 ✅ – effects of back emf ✅ DC Motors A DC motor is an electrical device that convert electrical energy into mechanical energy. In a DC motor, a current carrying coil of wire in a magnetic field experiences a force, F = nLIB. Initially the coil is alligned horizontally in a magnetic field. Sides AD and BC experiences no force since they are parallel to the magnetic field. Sides AB and CD are prependicular to the magnetic field and will experiences a force in opposite directions. These two forces will act together and cause the coil to rotate anticlockwise. There will be a magnetic force acting on every sideof the coil. However, the forces acting on sides AD and BC will be equal and opposite in direction Module 6: Electromagnetism 21 cancelling each other out. The forces on sides AB and DC remain and will continue to rotate the coil. When the coil reaches this position, forces acting on each side are such that they will tend to keep the coil in this position. The force will act outwards from each side of the coil. There are no turning force at this moment but any further rotation will cause the coil to rotate in opposite direction. For coil to continue anticlockwise, the current needs to be reversed. With this all forces are reversed and provided that coil has a little momentum to get it past perpendicular position, it will continue to rotate. Torque Torque is the turning moment of force. The net torque experiences by a coil in a DC motor is given by: where: = net torque (N m) n = number of loops in coil I = current (A) A = area of coil ( ) τ = nIAB sin θ τ m2 Module 6: Electromagnetism 22 B = magnetic field (T) = angle between area vector and magnetic field ( ) The area vector is normal to the plane of the coil. The torque is at maximum when the area vector is perpendicular to the magentic field and zero when the area vector is parallel to the magnetic field. The graphs of the force and net torque as a coil in a DC motor spins is shown below: Back EMF In DC motors, as coil rotates within a magnetic field it will be exposed to a change in magnetic flux which will induce an EMF (Faraday’s Law) called back EMF that creates its magnetic field to oppose the change in flux (Lenz’s Law). This induced current travels in opposition to the supplied emf. As motor spin faster, back emf increases and vice versa limiting current in the coil and its speed. When a load is applied to a motor, its speed decreases causing back emf to decrease and current to increase. θ ° ϵnet = V − ϵback Module 6: Electromagnetism 23 📖 analyse the operation of simple DC and AC generators and AC induction motors ✅ AC Induction Motors AC induction motors uses AC current. Stator consist of thin slotted, highly permeable steel lamination contained in a iron frame. Windings pass through slots of stator which enhance the magnetic field. When a 3 phase AC current runs sequentially through these windings, they produce a rotating magnetic field since AC is continuously changing its polarity and the windings are getting energised in pairs. The rotor consist of squirrel cage which is made from multiple skewed parallel bars positioned in the middle. Since the bars are experiencing a changing magnetic flux, it will cause an emf to be induced by Faraday's Law. By Lenz's law the emf will apply a current in a certain direction that will opposes the initial change in flux and the source of their motion. Hence the squirrel cage will rotate in the same direction as the magnetic field to reduce the relative motion between them. Module 6: Electromagnetism 24 Generators When coil is rotated, due to a change in magnetic flux a current is induced that creates a magnetic field to oppose the change in flux. The direction of this current is reversed every time plane of the coil is perpendicular to the field. AC Generators & Alternators The structure of an AC generator or alternator is identical to the structure of a DC motor except AC generators use slip ring commutators not a split ring Module 6: Electromagnetism 25 commutator. 3 phase generators exist that output a more constant maximum velocity. DC Generators DC generator structure is exactly the same as a DC motor. Split ring commutators are present that change direction of output so that output current is always in the same direction. Alternating Voltage & Current Module 6: Electromagnetism 26 📖 relate Lenz’s Law to the law of conservation of energy and apply the law of conservation of energy to: – DC motors and ✅ – magnetic braking ✅ Magnetic Braking When a metal plate is exposed to a changing magnetic field by Faraday’s law it will cause a current to be induced in the metal. The currents are named eddy currents and travel in a circle. By Lenz’s law these currents will be in such direction that they create a magnetic field that opposes the initial change in flux and apply a force that opposes its source of motion. This is the basic principle behind magnetic braking. As a metal plate moves or rotates in a magnetic field, mechanical work must be done to bring the disk to rest. As the plate begins to slow down induced eddy currents cause resistance heating. Hence the kinetic energy of the plate is converted to heat.