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## Electric Fields and Forces

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**Electric Fields and Forces**AP Physics B**Electric Charge**“Charge” is a property of subatomic particles. Facts about charge: • There are 2 types basically, positive (protons) and negative (electrons) • LIKE charges REPEL and OPPOSITE charges ATTRACT • Charges are symbolic of fluids in that they can be in 2 states, STATIC or DYNAMIC.**Electric Charge – The specifics**• The symbol for CHARGE is “q” • The unit is the COULOMB(C), named after Charles Coulomb • If we are talking about a SINGLE charged particle such as 1 electron or 1 proton we are referring to an ELEMENTARY charge and often use, e , to symbolize this. Some important constants:**Charge is “CONSERVED”**Charge cannot be created or destroyed only transferred from one object to another. Even though these 2 charges attract initially, they repel after touching. Notice the NET charge stays the same.**Conductors and Insulators**The movement of charge is limited by the substance the charge is trying to pass through. There are generally 2 types of substances. Conductors: Allow charge to move readily though it. Insulators: Restrict the movement of the charge Conductor = Copper Wire Insulator = Plastic sheath**Charging and Discharging**There are basically 2 ways you can charge something. • Charge by friction • Induction “BIONIC is the first-ever ionic formula mascara. The primary ingredient in BIONIC is a chain molecule with a positive charge. The friction caused by sweeping the mascara brush across lashes causes a negative charge. Since opposites attract, the positively charged formula adheres to the negatively charged lashes for a dramatic effect that lasts all day.”**Induction and Grounding**The second way to charge something is via INDUCTION, which requires NO PHYSICAL CONTACT. We bring a negatively charged rod near a neutral sphere. The protons in the sphere localize near the rod, while the electrons are repelled to the other side of the sphere. A wire can then be brought in contact with the negative side and allowed to touch the GROUND. The electrons will always move towards a more massive objects to increase separation from other electrons, leaving a NET positive sphere behind.**Electric Force**The electric force between 2 objects is symbolic of the gravitational force between 2 objects. RECALL:**Electric Forces and Newton’s Laws**Example: An electron is released above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel out the gravitational force on it. How far below the first electron is the second? Electric Forces and Fields obey Newton’s Laws. Fe e mg 5.1 m r = ? e**Electric Forces and Vectors**Electric Fields and Forces are ALL vectors, thus all rules applying to vectors must be followed. Consider three point charges, q1 = 6.00 x10-9 C (located at the origin),q3 = 5.00x10-9 C, and q2 = -2.00x10-9 C, located at the corners of a RIGHT triangle. q2 is located at y= 3 m while q3 is located 4m to the right of q2. Find the resultant force on q3. Which way does q2 push q3? Which way does q1 push q3? 4m q2 q3 3m Fon 3 due to 1 5m q q1 Fon 3 due to 2 q = 37 q3 q= tan-1(3/4)**Example Cont’**4m q2 q3 3m Fon 3 due to 1 5m q q1 F3,1sin37 Fon 3 due to 2 q = 37 q= tan-1(3/4) q3 F3,1cos37 5.6 x10-9 N 7.34x10-9 N 1.1x10-8 N 64.3 degrees above the +x**Electric Fields**By definition, the are “LINES OF FORCE” Some important facts: • An electric field is a vector • Always is in the direction that a POSITIVE “test” charge would move • The amount of force PER “test” charge If you placed a 2nd positive charge (test charge), near the positive charge shown above, it would move AWAY. If you placed that same charge near the negative charge shown above it would move TOWARDS.**Electric Fields and Newton’s Laws**Once again, the equation for ELECTRIC FIELD is symbolic of the equation for WEIGHT just like coulomb’s law is symbolic of Newton’s Law of Gravitation. The symbol for Electric Field is, “E”. And since it is defined as a force per unit charge he unit is Newtons per Coulomb, N/C. NOTE: the equations above will ONLY help you determine the MAGNITUDE of the field or force. Conceptual understanding will help you determine the direction. The “q” in the equation is that of a “test charge”.**Example**An electron and proton are each placed at rest in an external field of 520 N/C. Calculate the speed of each particle after 48 ns 8.32 x10-19 N 9.13x1013 m/s/s 4.98 x1010 m/s/s 4.38 x106 m/s 2.39 x103 m/s**An Electric Point Charge**As we have discussed, all charges exert forces on other charges due to a field around them. Suppose we want to know how strong the field is at a specific point in space near this charge the calculate the effects this charge will have on other charges should they be placed at that point. TEST CHARGE POINT CHARGE**Example**A -4x10-12C charge Q is placed at the origin. What is the magnitude and direction of the electric field produced by Q if a test charge were placed at x = -0.2 m ? 0.2 m E E 0.899 N/C -Q E E Towards Q to the right Remember, our equations will only give us MAGNITUDE. And the electric field LEAVES POSITIVE and ENTERS NEGATIVE.**Electric Field of a Conductor**A few more things about electric fields, suppose you bring a conductor NEAR a charged object. The side closest to which ever charge will be INDUCED the opposite charge. However, the charge will ONLY exist on the surface. There will never be an electric field inside a conductor. Insulators, however, can store the charge inside. There must be a negative charge on this side OR this side was induced positive due to the other side being negative. There must be a positive charge on this side**Electric Circuits**AP Physics B**Potential Difference =Voltage=EMF**In a battery, a series of chemical reactions occur in which electrons are transferred from one terminal to another. There is a potential difference (voltage) between these poles. The maximum potential difference a power source can have is called the electromotive force or (EMF), e. The term isn't actually a force, simply the amount of energy per charge (J/C or V)**A Basic Circuit**All electric circuits have three main parts • A source of energy • A closed path • A device which uses the energy If ANY part of the circuit is open the device will not work!**Electricity can be symbolic of Fluids**Circuits are very similar to water flowing through a pipe • A pump basically works on TWO IMPORTANT PRINCIPLES concerning its flow • There is a PRESSURE DIFFERENCE where the flow begins and ends • A certain AMOUNT of flow passes each SECOND. • A circuit basically works on TWO IMPORTANT PRINCIPLES • There is a "POTENTIAL DIFFERENCE aka VOLTAGE" from where the charge begins to where it ends • The AMOUNT of CHARGE that flows PER SECOND is called CURRENT.**Current**Current is defined as the rate at which charge flows through a surface. The current is in the same direction as the flow of positive charge (for this course) Note: The “I” stands for intensity**What is the current flowing through a battery if there is 30**coulombs charge flowing through the battery in 5 seconds. ?**There are 2 types of Current**DC = Direct Current - current flows in one direction Example: Battery AC = Alternating Current- current reverses direction many times per second. This suggests that AC devices turn OFF and ON. Example: Wall outlet (progress energy)**Ohm’s Law**“The voltage (potential difference, emf) is directly related to the current, when the resistance is constant” R= resistance = slope Since R=DV/I, the resistance is the SLOPE of a DV vs. I graph**Resistance**Resistance (R) – is defined as the restriction of electron flow. It is due to interactions that occur at the atomic scale. For example, as electron move through a conductor they are attracted to the protons on the nucleus of the conductor itself. This attraction doesn’t stop the electrons, just slow them down a bit and cause the system to waste energy. The unit for resistance is the OHM, W**Electrical POWER**We have already learned that POWER is the rate at which work (energy) is done. Circuits that are a prime example of this as batteries only last for a certain amount of time AND we get charged an energy bill each month based on the amount of energy we used over the course of a month…aka POWER.**POWER**It is interesting to see how certain electrical variables can be used to get POWER. Let’s take Voltage and Current for example.**If the there is a voltage drop of 10 volts as a charge has**100 joules work done on it , what is the charge ?**Other useful power formulas**These formulas can also be used! They are simply derivations of the POWER formula with different versions of Ohm's law substituted in.**Ways to Wire Circuits**There are 2 basic ways to wire a circuit. Keep in mind that a resistor could be ANYTHING ( bulb, toaster, ceramic material…etc) Series – One after another Parallel – between a set of junctions and parallel to each other**Schematic Symbols**Before you begin to understand circuits you need to be able to draw what they look like using a set of standard symbols understood anywhere in the world For the battery symbol, the LONG line is considered to be the POSITIVE terminal and the SHORT line , NEGATIVE. The VOLTMETER and AMMETER are special devices you place IN or AROUND the circuit to measure the VOLTAGE and CURRENT.**The Voltmeter and Ammeter**The voltmeter and ammeter cannot be just placed anywhere in the circuit. They must be used according to their DEFINITION. Current goes THROUGH the ammeter Since a voltmeter measures voltage or POTENTIAL DIFFERENCE it must be placed ACROSS the device you want to measure. That way you can measure the CHANGE on either side of the device. Voltmeter is drawn ACROSS the resistor Since the ammeter measures the current or FLOW it must be placed in such a way as the charges go THROUGH the device.**Simple Circuit**When you are drawing a circuit it may be a wise thing to start by drawing the battery first, then follow along the loop (closed) starting with positive and drawing what you see.**Series Circuit**In in series circuit, the resistors are wired one after another. Since they are all part of the SAME LOOP they each experience the SAME AMOUNT of current. In figure, however, you see that they all exist BETWEEN the terminals of the battery, meaning they SHARE the potential (voltage).**Series Circuit**As the current goes through the circuit, the charges must USE ENERGY to get through the resistor. So each individual resistor will get its own individual potential voltage). We call this VOLTAGE DROP. Note: They may use the terms “effective” or “equivalent” to mean TOTAL!**Example**R(series) = 1 + 2 + 3 = 6W A series circuit is shown to the left. • What is the total resistance? • What is the total current? • What is the current across EACH resistor? • What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately) DV=IR 12=I(6) I = 2A They EACH get 2 amps! V1W=(2)(1)= 2 V V3W=(2)(3)= 6V V2W=(2)(2)= 4V Notice that the individual VOLTAGE DROPS add up to the TOTAL!!**Parallel Circuit**In a parallel circuit, we have multiple loops. So the current splits up among the loops with the individual loop currents adding to the total current It is important to understand that parallel circuits will all have some position where the current splits and comes back together. We call these JUNCTIONS. The current going IN to a junction will always equal the current going OUT of a junction. Junctions**Parallel Circuit**Notice that the JUNCTIONS both touch the POSTIVE and NEGATIVE terminals of the battery. That means you have the SAME potential difference down EACH individual branch of the parallel circuit. This means that the individual voltages drops are equal. DV This junction touches the POSITIVE terminal This junction touches the NEGATIVE terminal**Example**To the left is an example of a parallel circuit. a) What is the total resistance? b) What is the total current? c) What is the voltage across EACH resistor? d) What is the current drop across each resistor? (Apply Ohm's law to each resistor separately) 2.20 W 3.64 A 8 V each! Notice that the individual currents ADD to the total. 1.6 A 1.14 A 0.90 A**Compound (Complex) Circuits**Many times you will have series and parallel in the SAME circuit. Solve this type of circuit from the inside out. WHAT IS THE TOTAL RESISTANCE?**Compound (Complex) Circuits**Suppose the potential difference (voltage) is equal to 120V. What is the total current? 1.06 A What is the VOLTAGE DROP across the 80W resistor? 84.8 V**Compound (Complex) Circuits**What is the current across the 100W and 50W resistor? What is the VOLTAGE DROP across the 100W and 50W resistor? 0.352 A Add to 1.06A 35.2 V Each! 0.704 A**Electrical Energy, Potential and Capacitance**AP Physics B**Electric Fields and WORK**In order to bring two like charges near each other work must be done. In order to separate two opposite charges, work must be done. Remember that whenever work gets done, energy changes form. As the monkey does work on the positive charge, he increases the energy of that charge. The closer he brings it, the more electrical potential energy it has. When he releases the charge, work gets done on the charge which changes its energy from electrical potential energy to kinetic energy. Every time he brings the charge back, he does work on the charge. If he brought the charge closer to the other object, it would have more electrical potential energy. If he brought 2 or 3 charges instead of one, then he would have had to do more work so he would have created more electrical potential energy. Electrical potential energy could be measured in Joules just like any other form of energy.**Electric Fields and WORK**Consider a negative charge moving in between 2 oppositely charged parallel plates initial KE=0 Final KE= 0, therefore in this case Work = DPE We call this ELECTRICAL potential energy, UE, and it is equal to the amount of work done by the ELECTRIC FORCE, caused by the ELECTRIC FIELD over distance, d, which in this case is the plate separation distance. Is there a symbolic relationship with the FORMULA for gravitational potential energy?**Electric Potential**Here we see the equation for gravitational potential energy. Instead of gravitational potential energy we are talking about ELECTRIC POTENTIAL ENERGY A charge will be in the field instead of a mass The field will be an ELECTRIC FIELD instead of a gravitational field The displacement is the same in any reference frame and use various symbols Putting it all together! Question: What does the LEFT side of the equation mean in words? The amount of Energy per charge!**Energy per charge**The amount of energy per charge has a specific name and it is called, VOLTAGE or ELECTRIC POTENTIAL (difference). Why the “difference”?**Understanding “Difference”**Let’s say we have a proton placed between a set of charged plates. If the proton is held fixed at the positive plate, the ELECTRIC FIELD will apply a FORCE on the proton (charge). Since like charges repel, the proton is considered to have a high potential (voltage) similar to being above the ground. It moves towards the negative plate or low potential (voltage). The plates are charged using a battery source where one side is positive and the other is negative. The positive side is at 9V, for example, and the negative side is at 0V. So basically the charge travels through a “change in voltage” much like a falling mass experiences a “change in height. (Note: The electron does the opposite)**BEWARE!!!!!!**W is Electric Potential Energy (Joules)is notV is Electric Potential (Joules/Coulomb)a.k.a Voltage, Potential Difference