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Transcript
Unit 2 – Electric and Magnetic Forces and fields Unit 2A–Electric Forces and Fields Electrical forces between static charges (stationary charges) have been known since 700BC. –Amber At the time of the renaissance, electricity was studied more completely. Electrified substances fell into 2 categories (positive and negative) while neutral substances formed a third category. These two categories are used to state the Law of Electric Charges1. opposite electric charges attract each other 2. similar electric charges repel each other 3. A charge object can attract some neutral objects!!!??? Why? To understand electrical charge, it is necessary to understand something about the structure of matter. 1. all matter is composed of atoms 2. Atoms are composed of smaller particles called electrons, protons and neutrons. a. Electrons are negative b. Protons are positive – same magnitude as electron c. Neutrons are neutral 3. Protons and neutrons are found in a tight cluster at the centre of the atom called the nucleus. Electrons are unclustered and occupy the remainder of the atom with great freedom of movement. 4. Protons and neutrons have about the same mass while an electron has about 1/2000 the mass of either. 5. Atoms are electrically neutral because the number of protons is equal to the number of electrons. 6. An atom can gain or lose electrons. Protons and neutrons are neitherlost nor gained without a nuclear reaction occurring! They are tightly bound in the nucleus. a. Substance that gains electrons is called a negative substance b. Substance that loses electrons is called a positive substance (net charge) explain qualitatively, the distribution of charge on the surfaces of conductors and insulators Conductors- materials in which electrons can move easily from atom to atom –mostly solids (why?), some liquids and gases (ionic-aq or capable of being ionized) -charge spreads out quickly in conductors to the best configuration for the repelling charges. -best conductors are metals. Insulators – materials in which electrons cannot move easily from atom to atom – some solids, many liquids, but most gases – why? -charge remains localized for insulators. (stays where you put it)eg. Balloon -they don’t transfer or release a charge very quickly. http://www.youtube.com/watch?v=LfJywoeIIUI conductor) (charges on a hollow Methods of Charging ****Electric charges on solids are due to an excess or shortage of electrons. Explain electrical interactions in terms of the law of conservation of charge Explain electrical interactions in terms of the repulsion and attraction of charges Compare the methods of transferring charge How to transfer a charge to an object: 1. Charging by friction Electrons are held in an atom by attraction to the nucleus. Depending on the types of atoms in a substance, it may have a stronger/weaker attraction to its electrons. When two materials of different strengths are rubbed together, the ‘stronger’ substance will take electrons from the weaker one leaving them both with net charges. - if it gained the electrons + if it lost them The two substance have equal, opposite charges!! – Law of conservation of charge. The two are attracted 2. Charging by conduction (contact) When one object already has a charge, it can be used to charge another object. This is done by bringing it into physical contact (touching) it to the other objects. Some of the electrons move and therefore some of the charge is transferred. The two objects collectively have the same charge as the original object (shared the charge). For our purposes, the two objects will be of the same material and so the charge is shared equally. Equal, same charges on the objects. (objects repel) However, what happens if the two objects are different materials? 3. Charging by Induction On a solid conductor, some of the negative charges are fairly free to move. If a charged object is brought near to the conductor, the electrons in the conductor will move giving the neutral conductor opposite induced charges on each of its sides. The neutral conductor can be given a permanent charge by grounding it while the charge object is nearby. Reverse scenario: When charged by induction, the once neutral conductor has a charge opposite to the charged object. (the two are attracted) What happens to the charge on the charged object??? Anything? How do the results of each method compare – similarities/differences? Problems pg 82-84 COULOMB’S LAW Explain qualitatively the principles pertinent to Coulomb’s torsion balance experiment Apply Coulomb’s law, quantitatively, to analyze the interaction of two point charges Determine, quantitatively, the magnitude and direction of the electric force on a point charge due to two or more other point charges in a plane Compare qualitatively and quantitatively, the inverse square relationship as it is expressed by Coulomb’s law and by Newton’s universal law of gravitation. Analyze data and apply mathematical and conceptual models to infer the relationship among charge, force and distance between point charges. Use free body diagrams. Use graphical techniques (such as straightening) to analyze data. Coulomb (1736-1806) used a torsion balance to study electrical forces. A thin metal wire is used to balance an insulating rod at its centre. On either end of the rod are two identical spheres which can be charged. Coulomb changed the distance between a charged rod and the torsion apparatus and measured the angle of twist in the apparatus. The amount of twist was considered proportional to the electrical force between objects. He found that Fα 1/d2. He also investigated the relationship between force (twist) and the magnitude of the charge on the rod. He found that Fα q1 q2. Combining these two results gives Coulomb’s Law for electrical forces; F = kq1q2/r2 k is Coulomb’s constant of 8.99 x 109 Nm2/C2. Use free-body diagrams to describe the forces acting on a charge in an electric field *Coulomb’s Law only applies to point charges. *Force is vector but it is often easier to use absolute values for charge and apply a direction to force after solving for the magnitude (absolute values). Eg. Two electrostatically charged 1 objects attract: 35o Three objects of different charges Interact. m=20g What if one objects distance or charge is changed? What happens to the force? Problems pg 86-94 Similarities/Differences to Fg – Newtons’ Law of Gravity -both vary inversely with the distance squared. -both involve a constant but the gravitational one is MUCH smaller -gravity is associated with mass, electrostatic is associated with charges. -gravity is always attraction, electrostatic can be attraction or repulsion. Graphs (straightening, slope to find k or q) Field Theory Define vector fields Compare forces and fields Explain, quantitatively, electric fields in terms of intensity (strength ) and direction, relative to the source of the field and to the effect on an electric charge Plot electric fields using field lines for point charges, combinations of point charges and parallel plates The concept of a field is used to explain how one object can influence or affect another object even when the objects are not in contact. The field theory is just a theory. A field is defined as a sphere of influence and may be scalar (magnitude only) or vector (magnitude and direction). Scalar fields include sound and heat while vector fields include gravity, electricity and magnetism. Electric Fields An electric charge exerts a force on anything around it. This region of influence is called a field – it is a vector field with both magnitude and direction. Because electric forces may be forces of attraction or repulsion, the direction of an electric field must be defined. (Unlike gravity) Since a field can be drawn/defined without having any object within the field, then the direction of an electric field is defined as the direction taken by a positive test charge placed within the field. Consequently the direction of an electric field is always away from the positive and towards the negative –regardless of what objects are in the field! Note: The strength of a field is represented by the density of the arrows and the direction of the field is represented by the direction of the arrows. What would determine how strong a field really is? -the amount of charge in the object -the distance from the object therefore: E=kq1/r2 where q is the charge on the object producing the field in question. DO NOT confuse E with energy!! It is electric field strength and distinguished by the arrow on top of it. This leads to a new formula: By replacing the same variable in the Fe equation, you get F=Eq problems pg 97-105 Potential Difference - Parallel Plates: Compare qualitatively, gravitational potential energy and electric potential energy Define electric potential difference as a change in electric potential energy per unit of charge Calculate the electric potential difference between two points in a uniform electric field Describe quantitatively the motion of an electric charge in a uniform electric field Explain, quantitatively, electrical interactions using the law of conservation of energy Analyze quantitatively the motion of an electric charge following a straight or curved path in a uniform electri field using Newton’s second law, vector addition and conservation of energy The equation for electric field; E=kq1/r2 and force; F = kq1q2/r2 are for static/point charges only. They cannot be used to describe the electric field between two charged plates. To describe the field between these plates we need the concept of potential difference. When charged objects are allowed to move in an electric field they always accelerate from a place of higher potential energy to a place of lower potential energy because of the electric force acting on it (like an object falling due to gravity). To move an object opposite to this requires work so we will incorporate the work formula: Work = force x distance W= Fe x d but Fe = q E so W=q E d Like with gravity, work done to move an object against the force is stored in the object as potential energy. So the increase in the potential energy is equal to the work! ∆Ep=q E ∆d When a charged object is placed in a uniform field, it will move from a place of high potential to a place of lower potential. It will lose potential and gain kinetic. Potential difference is defined as the change in potential energy per charge but can be calculated using either the change in potential or kinetic for a conservative system since what is gained in kinetic is lost in potential and vice versa (law of conservation of energy). ∆V = ∆E/q units for potential difference are J/C or V Potential difference is much more useful in electricity than kinetic/potential energy since it focuses on each charge instead of a total. Like energy, it is scalar. A battery is a source of PD. It is designed to move charges/ions from a place of high potential to a place of low potential, therefore creating movement of charges – electricity in a circuit. It converts chemical potential energy to electrical (kinetic) energy. Combining the two formulas learned today, we can come up with: E = ∆V/∆d another formula for calculating the electric field strength - this time, between parallel plates. Remember, the field strength is uniform (constant for a system)! battery symbol - + Eg. Problems pg 108-117 More Electric Plate Questions: Calculate the speed of the 3.50x10-12C sphere of mass +4.00x10-15kg just as it reaches the negative plate. 2.25x103V + - + An electron beam is projected between two parallel charged plates as shown below. There is a 2.80x103 N/C electric field between the plates. Calculate the horizontal distance the beam will travel before hitting the positive plate. Negative plate Electron beam 2.00 cm e- 6.00x106m/s 5.00 cm 3.00 cm Positive plate Physics Principles used to solve this question? MILLIKAN’S OIL DROP EXPERIMENT: Explain Millikan’s oil-drop experiment and its significance relative to charge quantization The electron was discovered by J.J. Thompson early in the 1900’s (Unit 4). Soon afterward Arthur Millikan found the charge on an electron called an elementary charge. It was discovered that an electron and a proton had charges of exactly the same magnitude. These discoveries were made by the use of parallel plates, electric force, and fields. How? Millikan sprayed oil droplets between two horizontal plates which were connected to a variable (adjustable) voltage source. The oil droplets were electrostatically charged from the spraying process so that when they were between the plates they were affected by opposing forces – gravity and electricity. Note: When dealing with parallel plates we don’t generally concern ourselves with gravity’s effect on the object because the electrical one is so much greater. However, Millikan used a low voltage source and oil drops (which have a much higher mass than a subatomic particle) so that the electrical force was very weak and gravity’s effects played an important role. By adjusting the low voltage source, Millikan was able to suspend some of the oil drops. For these suspended drops, Fe = F g Eq=mg q = mg/E How did Millikan find the mass on the oil drop? By using a ‘ruler’ behind the setup he could estimate the droplets diameter – allowing him to calculate the volume. Then using his oil’s density (mass/volume) he found the mass of the droplet. E was found using the voltage of the power supply and the distance between plates. g is constant From this formula, Millikan calculated a charge on the oil drop. This however could be any multiple of the elementary charge. So Millikan did the experiment many times and was able to determine that all the calculated charges were multiples of 1.60 x 10-19C. He therefore assumed that this was the smallest possible charge – elementary charge - the charge of an electron and proton. Problems pg 119-127 Review 131-133 CIRCUITS – Current/Voltage/Power Define electric current as the amount of charge passing a reference point per unit of time Current electricity involves new concepts because the charges are moving. Modern current electricity describes the flow of electrons (negative charge) based on our understanding of the atom and the ability for electrons to be released. Old theory described the flow of positive charge as being opposite to modern theory. This is called ‘conventional current’. (used in the textbook). Electrical Current: the rate at which electrons move through a conductor. The symbol for current is I and the unit is amperes (A). I = q/t One ampere = one coulomb/sec Electrons do not move through a conductor unless there is a potential difference. This potential difference that exists between the power supply entry/exit must be consumed within the circuit (by resistor(s)). For an electric current to operate there must be a voltage power source and a complete pathway for the charges. The amount of current in a circuit/conductor depends on the potential difference and the resistance of the conductor. More voltage more current (direct) Less resistance more current (inverse) I = V/R Resistance in a conductor (indicated by heat produced) depends on several factors: 1. Type of conductor –some hold onto their electrons more – more resistance 2. Cross-sectional area – smaller diameter of wire allows for less flow of electrons – more resistance 3. Length of conductor – longer conductor – resistance increases 4. Temperature - most conductors have an optimal temperature. Too high means random motion of electrons and vibration of atoms so that it is difficult for electrons to flow –higher resistance. Electrical Power: Power is the rate at which work is done or energy is used. Power is measured in watts (W) where one watt = one J/s P = W/t or ∆E/t In electricity ∆E =q∆V So: Unit 2B -Magnetic forces and fields: Describe magnetic interactions in terms of forces and fields Compare gravitational, electric and magnetic fields in terms of sources and directions Lodestone is a naturally occurring magnetic rock. A piece of lodestone will always line up in a north-south direction if it is free to move. Lodestone was studied extensively and it was concluded that Earth itself acted like a large lodestone and that was why a small piece of lodestone always lined up in a north-south direction. The ends of a magnet are called the N-pole (seeks earth’s geographic north) and a S-pole (seeks earth’s geographic south). There are two magnetic poles just as there are two kinds of electric charge. However, unlike electricity it is not possible to isolate one magnetic pole. Law of Magnetic Poles: 1. There are two kinds of poles, north and south 2. Like poles repel 3. Unlike poles attract Similar to electric charges, magnets have a region of influence called a magnetic field. Magnetic fields are vector fields (it has both magnitude and direction). The direction of a magnetic field is defined as the direction taken by a free north pole (*there is no such thing!). It is also the direction that the north end of a compass would point! S N S N S N N S S N N S S N Electric charges will affect small bits of almost anything in their electric field. Magnets, however, only affect a few materials (mainly metals) in their magnetic field. http://www.youtube.com/watch?v=NJUTUFAWfEY magnetic storm video Magnetism and Electricity: Describe how the discoveries of Oersted and Faraday form the foundation of the theory relating electricity to magnetism Describe, qualitatively, a moving charge as the source of a magnetic field and predict the orientation of the magnetic field from the direction of motion Oersted discovered a relationship between electricity and magnetism when he noticed that an electric current will deflect a compass needle. The only way this can happen is if an electric current produces a magnetic field. The field is circular around the wire. If the direction of the current is reversed, the direction of the field is reversed. 1st left hand rule: determines the direction of the magnetic field around a straight conductor. Hand is in relaxed position (curled) Thumb of left hand points in the direction of electron flow. Fingers circle the conductor in the direction of the magnetic field. X Out of page into page If the straight conductor is bent into a loop, the magnetic field inside the loop (coil) is made stronger. Increasing the number of coils also increases the strength of the field. This can create an electromagnet! Electromagnets: Electromagnets (solenoids) are made up of many loops of wire. Electromagnets act like permanent magnets except they can be turned on and off, and their strength can be easily adjusted. How? The field surrounding an electromagnet is stronger inside the coil and weaker outside the coil. The field also runs in opposite directions inside vs outside the coil. *electromagnet needs an insulator between the coils and a conducting core to prevent current from flowing the shortest path through the core conductor. 2nd left hand rule: determines the direction of the field for an electromagnet. Hand is in relaxed position (curled) Fingers of left hand curl around the coil in the direction of electron flow. Thumb points to the direction of the electromagnet’s north pole. (this is the direction of the field inside the coil and opposite to the field outside the coil) Magnetic Fields/forces around Conductors (moving charges): Describe and explain, qualitatively, the interaction between a magnetic field and a moving charge and between a magnetic field and a current-carrying conductor Explain, quantitatively, the effect of an external magnetic field on a current-carrying conductor Design an experiment If two straight conductors are running parallel and are carrying current in the same direction, they will attract one another: If they have current in the opposite directions they will repel one another: The unit of current was actually defined in terms of this effect: One ampere is the amount of current in each of two conductors that are one meter apart and cause a force of 2 x 10-7 N to act on each meter of wire. When two magnetic fields are overlapping, they will interact and create a force. Another example of this is: Below the conductor, the two fields have the same direction so they will repel. Above the conductor the fields are opposite and will attract. The net result is that the conductor is forced upwards (deflected). Oersted discovered this relationship between current and magnetic fields. A short cut for determining the direction of deflection is the 3rd left hand rule: Flat hand is used Fingers are pointed in the direction of the permanent magnetic field. Thumb points in the direction of the current flow (or particle velocity) Palm faces the direction of deflection. Note: all three are perpendicular to each other. Electric Motors make use of this interaction in order to convert electrical energy (current) into mechanical energy (movement). In the motor, a loop of wire (armature) becomes an electromagnet when the current is turned on. This armature is placed in a permanent magnetic field and so the two fields interact and cause a force that results in the movement of the armature. Motor Effect Because of the split-ring commutator and brushes, the polarity of the armature reverses every 180o. This allows the armature to constantly be repelled and continue to turn. (However, if an AC power supply is used, then the motor does not need the split ring commutator since the current is constantly reversing direction.) To calculate the force of deflection on a conductor in a magnetic field: Fm = B I l Moving Charges in Magnetic Fields: Explain, qualitatively and quantitatively, how a uniform magnetic field affects a moving electric charge, using the relationships amoung charge, motion, field direction and strength, when motion and field directions are mutually perpendicular Explain, quantitatively, how uniform magnetic and electric fields affect a moving electric charge, using the relationships amoung charge, motion, field direction and strength, when motion and field directions are mutually perpendicular Analyze, quantitatively, the motion of an electric charge following a straight or curved path in a uniform magnetic field, using newton’s second law and vector addition Analyze, quantitatively, the motion of an electric charge flowing a straight path in uniform and mutually perpendicular electric and magnetic fields, using Newton’s second law and vector addition. Use free-body diagrams to describe forces acting on an electric charge in electric and magnetic fields. Charges passing through magnetic fields may also be deflected by the magnetic field in the same way as charges in a conductor. To determine the direction of deflection use the 3rd rule and apply it to your left hand for negative particles and your right hand for positive particles. The magnetic force is: Fm = B q v In a strong magnetic field they may be deflected so much that they end up travelling in a circle: In this case Fm = Fc Charged particles in space are often deflected by Earth’s magnetic field. Some of the particles are trapped in a spiral. When they reach the atmosphere they collide with the gas molecules causing them to glow. This creates the Aurora (northern/southern lights) near the poles of Earth. Why would this not occur at other latitudes? Electromagnetic induction: (Generator effect) Describe, qualitatively, the effects of moving a conductor in an external magnetic field, in terms of moving charges in a magnetic field. Design an experiment After Oersted’s discovery that an electric current produced a magnetic field, it was discovered that a magnetic field could produce an electric current . An electric current can be produced in a conductor by moving the conductor through a magnetic field. A voltage is induced across the conductor. If the conductor is part of a circuit it will act like a battery. Producing an induced voltage in a conductor using a magnetic field is known as Electromagnetic Induction. A current can be produced in an air core solenoid when a magnet is moved in or out of the core. (demo) When the magnet changes direction so does the current. The direction of the induced current can be found using Lenz’ Law; the magnetic force on a conducting rod is in the opposite direction to its motion (the applied force). Eg. When a magnet is pushed into a coil a current will move in a direction such that the magnetic field inside the coil opposes the magnetic field of the magnet. This must occur in order to satisfy the conservation of energy principles. The two fields must oppose one another or else you would be creating more energy! Rod moved through a magnetic field will produce an electric current: Loop of rod (generator) 4th left hand rule: used to find the direction of the induced current. Use a flat hand The palm is pointed opposite to the velocity of the rod. Fingers point in the direction of the magnetic field Thumb will point in the direction of the induced current in the rod. The strength of the current depends on the speed of the rod/magnet, the amount of conducting rod/wire in the permanent field, and the strength of the permanent field. Another way to produce an electric current is by using an induction coil. Michael Faraday used this to generate a brief current when the switch was being closed or opened. The current needs to be changing to cause the magnetic field to fluctuate in the soft iron core AC current . This changing magnetic field is similar to moving a magnet and therefore causes an induced AC current on the secondary side. A transformer (induction coil) is often used to convert a potential difference to a higher or lower value. Primary coil – connected to the power supply. Secondary coil – no power supply – current is generated by induction. If the number of coils on the secondary side is more than the primary, the potential difference is increased on the secondary side. This is called a step-up transformer. Eg. TV If the number of coils on the secondary side is less than the primary, it is called a step-down transformer. Eg. Transformer boxes outside your home. However, like lenz’ law, you can’t create more energy! So if we can increase the potential difference by increasing the # of coils, something has to decrease – current! This means the power/energy remains constant. Levitating car: http://mail2.myghsd.ca/owa/redir.aspx?C=87016bfa1f91481587a82f1 61cc76251&URL=http%3a%2f%2fwww.flixxy.com%2fvolkswagenlevitating-car.htm