# Chapter 8. Electricity and Magnetism. Law of Charges. Negative/Positive

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1 Chapter 8 Electricity and Magnetism Electricity and Magnetism (1) Electric Charge Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Protons positive charge Electrons negative charge Negative/Positive An object with an excess of electrons is said to be negatively charged An object with a deficiently of electrons is said to be positively charged Law of Charges Law of Charges like charges repel, and unlike charges attract Two positives repel each other Two negatives repel each other Positive and negative attract each other The force between two charged bodies is directly proportional to the product of the two charges & inversely proportional to the square of their distance apart. Section Section

2 Repulsive and Attractive Electrical Forces Two negative charges repel Two positive charges repel One negative and one positive attract Repulse Repulse Attract Section Inverse Square Law Newton s Universal Law of Gravitation

3 Coulomb (C) = Unit of Electric Charge Named after a French scientist Charles Coulomb ( ) Note that the charge on a single electron (-) or proton (+) is 1.60 x C (very small!) q usually designates electric charge Excess of positive charges +q Excess of negative charges -q Coulomb s Law Force of attraction/repulsion between two charged bodies is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them F = (kq 1 q 2 ) / r 2 F = force of attraction or repulsion q 1 = magnitude of the first charge q 2 = magnitude of the second charge r = distance between charges k = constant = 9.0 x 10 9 N-m 2 /C 2 Section Section Comparison of Coulomb s Law & Newton s Law of Universal Gravitation A stationary wire with no current will not experience a force in a magnetic field Equations look similar F = kq 1 q 2 / r 2 & F = Gm 1 m 2 / r 2 Both depend on r 2 Coulomb s law can describe either an attractive or repulsive force gravity is always positive Electrical charges are much stronger than gravitational forces Section Section

4 A current-carrying wire in a magnetic field experiences a force, out of the page as shown here Motors Electric motor a device that converts electrical energy into mechanical work When a loop of coil is carrying a current within a magnetic field, the coil experiences a torque and rotates Section Section Generators Generator a device that converts mechanical energy into electrical energy Generators operate on the principle of electromagnetic induction Electromagnetic induction was discovered by the English scientist, Michael Faraday in 1831 When a magnet is moved toward a loop or coil of wire, a current is induced in the wire The same effect is obtained if the magnetic field is stationary and the loop is rotated within it Electricity and Electric Circuits Definitions First Section

5 Current time rate of flow of electric charge I = charge/time = q/t I = electric current (amperes) q = electric charge flowing past a point (coulombs) t = time for the charge to pass point (seconds) 1 ampere (A) = flow of 1 Coulomb per second Rearrange equation above: q = It or 1 coulomb = 1 ampere x 1 second Therefore, 1 coulomb is the amount of charge that flows past a given point in 1 second when the current is 1 ampere Conductors/Insulators Electrical conductor materials in which an electric charge flows readily (most metals, due to the outer, loosely bound electrons) Electrical insulator materials that do not conduct electricity very well due to very tight electron bonding (wood, plastic, glass) Semiconductor not good as a conductor or insulator (graphite) Section Section Electric Potential Energy When work is done to separate positive and negative charges, we have electric potential energy Voltage Instead of measuring electric potential energy, we measure the potential difference, or voltage Voltage the amount of work it would take to move a charge between two points, divided by the value of the charge Voltage = work / charge = V = W/q Measured in volts (V) = 1 joule/coulomb When we have electric potential energy, this may be used to set up an electrical current Section Section

6 Ohm s Law (1) Ohm s Law Analogy Whenever there is an electrical current, there is resistance (R) within the conducting material R is due to atomic/subatomic collisions Georg Ohm ( ) formulated a simple relationship between voltage, current, and resistance Water Pressure = Voltage Hot / Cold valves = Resistance Water flow = Current Section Ohm s Law Analogy Current Flow Current Flow Resistance Voltage Resistance Voltage

7 Series R = R 1 + R 2 + R 3 Parallel R R R R Ohm s Law (2) Ohm s Law V = IR V = voltage in volts I = current in amperes R = resistance in ohms 1 ohm = 1 volt/1 ampere (R=V/I) Simple Electrical Circuit Electrons flow from negative terminal to positive terminal (provided by the chemical energy of the battery) -- negative to positive Open switch not a complete circuit and no flow of current (electrons) Closed switch a complete circuit and flow of current (electrons) exists Closed Circuit Required to have a sustained electrical current Section Section

8 Electrical Circuit & Waterwheel Analogy Simple Electrical Circuit The light bulb offers resistance. The kinetic energy of the electric energy is converted to heat and radiant energy. Section Section Electrical Power (2) P = IV (Electric power = current x voltage) also P = I 2 R (substitute in V = IR) P in watts, I in amperes, R in ohms, V in volts Forms of Electric Current Direct Current (dc) the electron flow is always in one direction, from (-) to (+) Used in batteries and automobiles Alternating Current (ac) constantly changing the voltage from positive to negative and back Used in homes. 60 Hz (cycles/sec) and Voltage of V Section Section

9 Simple Electric Circuits in Series Plugging appliances into a wall outlet places them in a circuit either in series or in parallel In a series circuit, the same current (I) passes through all the resistances. The total resistance is simply the sum of the individual resistances. Series Circuit R s = R 1 +R 2 +R 3 + If one bulb were to burn out the circuit would be broken, and all the lights would go out Same current all the way Section Section Simple Electric Circuits in Parallel In a parallel circuit, the voltage (V) across each resistance is the same, but the current (I) through each may vary. Parallel Circuit I = I 1 +I 2 +I 3 + for R in parallel: 1/R p = 1/R 1 +1/R 2 + for 2 R in parallel: R p = (R 1 R 2 )/(R 1 + R 2 ) Current Divides, Voltage is the same Section Section

10 Magnetism Magnetic Fields Closely associated with electricity is magnetism. In fact electromagnetic waves consists of both vibrating electric and magnetic fields. These phenomena are basically inseparable. A bar magnet has two regions of magnetic strength, called the poles. One pole is designated north, one south. Section Magnetic Poles The N pole of a magnet is north-seeking it points north. The S pole of a magnet is south-seeking it points south. Magnets also have repulsive forces, specific to their poles, called Law of Poles Like poles repel and unlike poles attract N-S attract S-S & N-N repel Section

11 Law of Poles All magnets have two poles they are dipoles Magnetic Field Magnetic field - a set of imaginary lines that indicates the direction in which a small compass needle would point if it were placed near a magnet These lines are indications of the magnetic force field. Magnetic fields are vector quantities. Section Section Magnetic Field The arrows indicate the direction in which the north pole of a compass would point. Electromagnets A simple electromagnet consists of an insulated coil of wire wrapped around a piece of iron. Stronger current stronger magnet Electromagnets are made of a type of iron that is quickly magnetized and unmagnetized termed soft. Section Section

12 Earth s Magnetic Field This planet s magnetic field exists within the earth and extends many hundreds of miles into space. The aurora borealis (northern lights) and aurora australis (southern lights) are associated with the earth s magnetic field. Although this field is weak compared to magnets used in the laboratory, it is thought that certain animals use it for navigation. Earth s Magnetic Field Similar to the pattern from a giant bar magnet being present within the earth (but one is not present!) Section Section Earth s Magnetic Field The origin of the earth s magnetic field is not completely understood. Probably related to internal currents of electrically charge particles in the liquid outer core of the earth, in association with the earth s rotation The temperatures within the earth are much hotter than the Curie temperature, so materials cannot be ferromagnetic. The positions of the magnetic poles are constantly changing, suggesting currents. Chapter 8 - Important Equations F = kq 1 q 2 /r 2 Coulomb s Law I = q/t Current V= W/q Voltage V= IR Ohm s Law P= IV = I 2 R Electric Power R s = R 1 + R 2 + R 3 Resistance in Series 1/R p = 1/R 1 + 1/R 2 + 1/R 3. Resistance in Parallel R p = (R 1 R 2 )/(R 1 + R 2 ) Two Resistances in Parallel Section Review

13 Chapter 8 Equations for the Test V= IR Ohm s Law P= IV = I 2 R Electric Power R s = R 1 + R 2 Resistance in Series R p = (R 1 R 2 )/(R 1 + R 2 ) Two Resistances in Parallel Questions 13. How much does it cost to run a 1500-W hair dryer 30 minutes each day for one month (30 days) at a cost of 12 per kwh? Review Questions 19. Two resistors with values of 25 Ω and 35 Ω, respectively, are connected in series and hooked to a 12-V battery. a. How much current is in the circuit? b. How much power is expended in the circuit? Questions 20. Suppose the two resistors in Exercise 19 were connected in parallel. What would be: a. The current in the circuit? b. The power expended in the circuit?

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