A field is an invisible area of influence around an object If you place another object in the field it will experience a force 1 object is said to be causing the field The object experiencing the field is called the TEST OBJECT
Newton s Apple
We often use field lines to represent the strength, direction and shape of field
Newton s Universal Law of Gravity Isaac Newton was the first to mathematically define gravity as a universal force. His Universal Law of Gravity states: All objects with mass exert a force of attraction on all other objects with mass. F g
Asteroid Itokawa, an asteroid that is a loose pile of rubble rather than solid rock.
The strength of Earth s gravity field depends on the distance from the centre of Earth and on the types of rocks beneath the surface
The units of gravitational field strength is N/kg N/kg = m/s 2 Average value of g near surface of Earth is 9.81 N/kg or 9.81 m/s 2
The larger the masses the larger the gravitational field g The greater the distance separating the objects, the smaller the force of gravity. r = the distance between the objects
g r There is an inverse square relationship between the force of gravity and the distance between the objects. r e.g. if the distance is doubled, the gravitational force reduces to one quarter its original strength.
r Mass of object producing the field
Force of gravity acting on object F g mg Mass of test object (object experiencing the field)
Example Problem 1: a) Calculate gravitational field strength at the surface of earth. (Look up mass of earth and radius of earth on your data sheet!) b) Calculate the force of gravity exerted by the earth on little Frankie (m=10.0 kg) sitting on the surface of Earth. r
Solution A. g g Gm 2 r 6.67 10 11 N m 2 kg 2 6 6.37 10 m 2 5.98 10 24 kg = 9.83N/kg
Calculator Entry 6.67E-11x5.98E24/6.37E6x 2 9.82987.
Solution B. F g m g F g 10.0 kg(9.83 m / s ) 2 98.3N
2) The moon has a mass of 7.35 x 10 22 kg. The radius of the moon is 1737 km. Calculate the gravitational field strength on the surface of the moon.
g g Gm r 2 Solution N m 2 11 22 2 6.67 10 7.35 10 kg 1737 10 3 m 2 kg g 1.62 N / kg
3) A satellite experiences a gravitational strength of 1.5 N/kg. Calculate its altitude above Earth s surface.
Solution g Gm r 2 r 2 Gm g r 2 Gm g r Gm g
_ Solution r 6.67E 11 5.98E24 /1.5 r 16306797.51 m This is from centre of Earth
Solution _ r 6.67E 11 5.98E24 /1.5 r 16306797.51 m This is from centre of Earth 16306767.51 m 6.37 x 10 6 m = 9.9 x 10 6 m
Example 4 The gravitational attraction between two masses is 36.0 N. What will the new force be if the distance between the objects is tripled? g r 1 2 Gravity gets weaker as distance gets larger So force of gravity gets weaker too F g 1 2 r
New force New force 36.0 N 36.0 N 1 3 2 1 3 2 Solution 36.0 N 36.0 N 1 change 1 in r 36.0 N 1 change 4.00in Nr 9 36.0 N 1 9 4.00 N 2 2
All atoms are made of Positive protons and neutral neutrons in the nucleus Negative electrons outside the nucleus Like charges repel Opposite charges attract
In conductors (most conductors are metals) some electrons are free to move, while the positive nuclei are stuck in place.
When two different substances are rubbed together, electrons can be transferred from one substance to another. When charges are separated, electrical potential energy is stored (called a VOLTAGE)
the electrical energy is released when a current of electrons flows back
Some materials hold onto electrons more tightly than other materials One substance gains electrons becoming negatively charged. The other substance loses electrons and becomes positively charged The total amount of charge doesn't change (charge is conserved)
Van de Graff Generators build up charge using friction
ELECTROSCOPES used to detect the presence of an electric charge The further apart the leaves, the greater the charge. Recall that like charges repel and opposite charges attract
A positively charged rod is placed near an electroscope Electrons in the leaves move toward head, leaving the leaves positive When the rod is removed, the leave return to their original position During the whole process, the electroscope is neutral + + + - - - - + + - + - - + - + + - - + + - - + + + Electric Force (Repulsion) + + +
The leaves also spread apart when a negative object is placed near by. The electrons travel into the leaves because they are repelled by the negatively charged rod. The negatively charged leaves are subsequently repelled by each other and move apart. - - - - + + + - - - - + + - + - - - - - - - - + - + + - - + + + - Electric Force (Repulsion) - - - -
If a positively charged object touches a neutral object, some of the free electrons from the neutral object will move to the positively charged object + e - Neutral object e - + positive + e - e - + + Positive object + + +
ELECTRIC FORCE Charles Coulomb (1736-1806) used a torsion balance to determine the nature and strength of the electric force
We now measure the size of the charge in units called Coulombs (C) Coulomb found: The larger the charge the greater the electric force The greater the distance between the charges the weaker the force
He found an INVERSE SQUARE relationship between force and distance between the charges.
ELECTRIC FIELDS Michael Faraday developed the idea of lines of force to describe electric fields. A field is a sphere of influence in which a force can affect an object at a distance without contact.
The electric field strength is a vector (it has a direction) A spherical point-source field
The direction of the field is defined as the direction of the electric force acting on a positive test charge. + +
More field lines indicate a stronger field The further you get from the charge, the weaker the field
g E r E r r Just like the gravitational field strength, there is an INVERSE SQUARE RELATIONSHIP between electric field strength and the distance from the charged object.
ELECTRIC FIELDS WITH TWO CHARGES Field lines always begin at positive charges and end at negative charges. If a charge is placed in the field, and is free to move, it will move along a field line. +
Two like charges
+
Two opposite charges
The Shape of a Conductor can affect electric field strength The charges spread out evenly on the surface. The field is stronger near the sharp corners
CALCULATING ELECTRIC FIELD STRENGTH Charge of object producing the field
Practice Determine the electric field strength 2.00 x 10-6 m from a proton. q = 1.60 x 10-19 C k = 8.99 x 10 9 N C 2 /m 2
The field between the wire cage and the rod is strong enough to cause charges to flow through the air.
Example 1 Find the magnitude of the electric field at a point 0.450 m from a 5.00 x 10-6 C charge. Ans: 2.22 x 10 5 N/C
Example 2 The electric field strength is 195 N/C at a distance of 50 m from a storm cloud. Calculate the charge of the storm cloud. Ans: 5.4 x 10-5 C
Example 3 A balloon has an electrical charge of 5.82 μc. Calculate the distance from the balloon where there is a an electric field strength of 100 N/C. Ans: 22.9 m
Example 4 Determine the magnitude and direction of the electric field at point P. 36 N/C Left -10 C
PERMANENT MAGNETS Only some metals experience a noticeable force when placed in a magnetic field Most contain Fe, Co, or Ni
Magnetic fields are caused by moving charges. In permanent magnets, electron spinning causes magnetic fields. The atoms of permanent magnets are arranged in small structures called domains (~1 mm) where the electrons are spinning in the same direction Each domain acts like a small magnet
Some materials do not form magnetic fields, because the domains are random In some materials, the domains are organized so that the magnetic field of each domain add up to a larger magnetic field
Each magnets exists as a north and south pole pair. Poles can t exist on their own. Opposite poles attract Like poles repel
Domains may be temporarily aligned by an external magnetic field (TEMPORARY MAGNETS) The domains of a magnet can be scrambled by heat, shock or other strong magnetic fields.
Field lines leave the north pole and enter the south pole Field lines always form closed loops
The magnetic field is a vector The direction is determined by the direction a northpointing compass needle Field lines always form closed loops
Earth s Magnetic Field The geographic north pole is actually the magnetic south pole
Compasses point north because they are attracted to a south magnetic pole
Due to dynamic processes inside the earth, the magnetic poles are on the move
Charged particles ejected from Sun in solar flares
Earth s magnetic field deflects high-speed charged particles called solar wind which are ejected from the sun.
Charged particles from the sun and outer space become trapped in a part of the earth s magnetic field The particles collide with gas exciting them to release energy in the form of light producing the northern and southern lights
ELECTRICAL CURRENTS CAUSE MAGNETIC FIELDS moving electrons cause magnetic fields The magnetic field is circular around the wire and always at right angles to the wire.
Coiling the wire results in the fields of each loop adding together to make a large, uniform field inside the coil
The magnetic field of a coil (aka: solenoid) is very similar to the field of a bar magnet Solenoid: a coil of wire The field strength get stronger with more loops
Magnetic Resonance Imaging (MRI) Uses radio waves & electromagnetic coils to image the inside of the body
GENERATORS, MOTORS, and TRANSFORMERS
Electromagnetic Induction A moving magnet can cause a current to flow in a nearby conductor (induces a current) A changing magnetic field can also induce electricity in a conductor
To generate electricity, you can spin a turbine move a magnet near a conductor move a conductor near a magnet
Most generators involve coils of wires spinning inside a large magnetic field Kinetic (mechanical) energy is converted to electrical energy.
Spinning motors produce ALTERNATING CURRENTS
Alternating Current (AC): the size and direction of current flow varies with time Standard electrical outlets supply AC current at a frequency of 60 Hz and a average voltage of 120 V
Simple Generator Output (DC)
There are many ways to spin a generator: Examples: Wind turbine Hydro electric High pressure steam (coal, natural gas, nuclear, solar mirrors)
Direct Current (DC): the direction of the current is constant Supplied by batteries or solar cells
How Batteries Work: A chemical reaction releases electrons which flow from the negative end to the positive end The amount of energy provided to each coulomb of electrons is is called electrical potential or voltage (V) When a conductor connects the positive and negative ends, a circuit is formed and electrons flow as current through the conductor.
Solar Cells (Photovoltaic cells) convert light energy directly into electrical energy in the form of DC current
V DC from Photocells and batteries
ELECTRIC CURRENT Current (A) or (C/s) Moving charges are known as an electric current Current is the flow rate of electrons the amount of charge that passes a point in the circuit per second 1 Ampere = 1 Coulomb/second Time (s) Charge (C) Which has the larger current? The electrons actually move very slowly (cm s per second)
Electrons flow through conductive wires because one end is negative and the other end is positive. The current depends on the potential difference and the resistance of the conductor
CONDUCTORS VS. INSULATORS INSULATORS (don t allow electrons to move) Glass Air Plastic Rubber wood CONDUCTORS (allow electrons to move) Copper Aluminum Gold Silver Platinum Solutions that conduct electricity are called electrolytes
Circuit Diagrams Standard symbols: cell + - switch Bulb Wires connected Wires not connected Ammeter Resistor Fuse Voltmeter A resistor is any device that converts electrical potential energy into other forms of energy, such as heat or light
Circuit Diagram
SERIES CIRCUITS Components connected one after the other There is only one path for the current to travel
PARALLEL CIRCUITS There is more than one path for the current to flow
Meters A voltmeter measures the potential difference between two points in a circuit so it must be connected in parallel Ammeters measure current at a single point and must be connected in series. (Connecting an ammeter in parallel may cause damage to the device)
ELECTRICAL RESISTANCE No wire is a perfect conductor. There is always some friction applied to the current flow.
Factors that affect resistance: 1)Type of material Metals have low resistance some materials have virtually no resistance
2) Length of the conductor: the longer the conductor, the greater the resistance 3) Diameter of the conductor: the greater the diameter, the lower the resistance 4) Temperature: resistance increases as temperature increases.
Resistors are often used to control the amount of current in circuits
OHM S LAW: The current in an electric circuit is directly proportional to the voltage The current is inversely proportional to the resistance Geog Simon Ohm (1787-1854) Voltage (V) Current (A) Resistance (Ohms - Ω)
Example 1 A 100 Ω resistor is connected to a 12.0 V battery. Determine the current flowing in the resistor. I V I = 0.120A R
Example 2 A circuit has 36.0 ma flowing in it when it is connected to a 13.5 V power supply. Determine the resistance of the circuit. R = 375 Ω R R V I 13.5V 36.0 10 3 A
WATT S LAW The power in an electric circuit is measured in watts and depends on the electrical potential and the current Power (W) or (J/s) Current (A) James Watt 1736-1819 Voltage (V)
Also: P I 2 R Useful for determining the power dissipated by a resistor, light bulb, etc.
Examples 1. Determine the current flowing in a 100 W light bulb connected to 120 V 2. Which light bulb has the greatest resistance: a 100 W bulb or a 17 W bulb? Both are connect to 120 V
Potential Difference (V) The slope of a voltage-current graph is the resistance V rise R I run Current (x 10-3 A)
TOTAL RESISTANCE with more than 1 resistor Each resistor connected in series has the same current flowing through it. The total resistance is the sum of the resistance of each resistor.
e.g. Calculate the total resistance of the circuit below. R 1 = 2.5 k R 2 = 1.0 k R 3 = 3.0 k R T = 6.5 k
When resistors are connected in parallel, the currents can be different in each resistor The total resistance will be less than the smallest individual resistor To find the total resistance of parallel resistors:
e.g. Calculate the total resistance of the circuit below. Example R1 = 1 k = 1000 R2 = 2.5 k = 2500 R3 = 3 k = 3000 R T =?
Use x -1 button on calculator 1 1000 2500 3000 R 1 1 1 Calculator gives 1 R 0.00173333333
Use the x -1 again to get the answer R 0.00173333333 1 R = 577
Example: A 100 Ω, 200 Ω, and a 400 Ω resistor are connected in parallel to a 12.0 V battery. Find the total resistance and current in the circuit. R T = 57.14 Ω I= 0.210 A
The current in each resistor is 3.5 A. What is the total current in the circuit?
Which would have the most current: bulb, 15.0 or 10.0 resistor?
What is the total resistance of the circuit?
Energy in electric circuits E = Pt E (energy) in Joules P in watts t in seconds t E P
Energy in the home Your power bill charge for energy is in units called kilowatt hours (kwh) kwh is using 1000 W every hour
Energy Usage in the Home Example: A 20 W electric nose trimmer is used for 15 hours. How much does this cost if Epcor is charging 8 /kw h? E = Pt in data book, p 3 E = 20 W x 15 hours = 300 W h = 0.300 kw h Cost = energy x price Cost = 0.300 kw h x 8 /kw h Cost = 2.4
Series and Parallel Circuits The voltages across series resistors must add to the supply voltage. 12 V R 1 = 10 R 2 = 20 R 3 = 40 Find the total current in the circuit and then the voltage across each resistor
The voltage across parallel resistors must be the same
FUSES & BREAKERS Both shut off circuits when the current reaches dangerous levels (the heat given off can start fires) Fuses have a filament that melts, shutting off the circuit The fuse must be replaced
Breakers use an electromagnetic switch to turn off the circuit when the current gets too high. Flipping the breaker switch reactivates the circuit
Household Circuits breaker Main breaker breaker
ELECTRICAL DISTRIBUTION & TRANSFORMERS Transformers use a changing current in one coil to produce a changing current in another coil The major use of transformers is to change the current and voltage values from the input side to the output side
Generating stations use transformers to step up voltages (reduces current), before sending the energy to the city on large diameter (low resistance) wires P = I 2 R
The power dissipated in the wire depends on the square of the current, less energy is wasted heating up the transmission lines when voltage is high, rather than current P = I2 R
Genesee Power Plant Voltage is stepped up to 500 kv using transformers (225 tonnes)
Transformer theory Transformers are basically two coils of wire wound on an iron core The coils are wound on an iron core to concentrate the magnetic field
There is no electrical connection between the coils. They interact only through a changing magnetic field
A changing magnetic field around the primary causes a changing current in the secondary An alternating current (AC) is required as the input AC currents constantly change, and therefore induce constantly changing magnetic fields
The voltage can be stepped up (increased) from the primary to the secondary, or it can be stepped down (decreased) Energy must be conserved: the power must be equal in the primary and the second. (very little power is lost from primary to secondary because of inefficiency)
e.g. if the voltage is increased by a factor of 3, the current is decreased by a factor of 3. P IV 1 3 3 P I V ( )
CALCULATIONS WITH TRANSFORMERS For ideal (100% efficient) transformers: Number of turns in the coil Voltage in the coil (V) Current in the coils (A)
Example A transformer has 350 turns on its primary and 5600 turns on its secondary. If the primary is connected to 120 V AC, what would the secondary voltage be? N N p s V V 350 5600 p s 120V V s V s = 1.92 x 10 3 V
Example A transformer is connected to a 120 V source and has 0.126 A in the primary. If the output voltage is 13.6 V, what is the secondary current? V V p s 120V 13. 6V I I s p I s 0. 126A I s = 1.11 A
Example D.J. Trump wants to use a very long extension cord in his huge new back yard. The current will be 6.80 A and the resistance of the cord is 19.1. How much power will be dissipated by the extension cord? 883 W (almost as much heat as nine 100 W bulbs!)
Motors Convert electrical energy into mechanical energy (opposite of generators)
1. Armature (rotating electromagnet) 2. Commutator: to connect brushes to the armature 3. Battery 4. Brushes slide against commutator to make an electrical connection
1. Current flows in armature causing an electromagnet 2. One side of armature is attracted to the N pole, other side to S pole 3. Armature rotates, commutator causes armature to switch poles (#1 now becomes a south pole so is repelled)
Generator Armature is rotated by falling water, a turbine, a windpowered propeller etc.
Moving coil has electricity induced in it Brushes slide against commutator to make an electrical connection battery is recharged
Voltage Simple DC Generator
Voltage Alternator (AC)
How a DC motor works: Motors
AC motors don t require commutators
An AC Motor: