# Unit 5 - Fields Chapter 14 Chapter 15. Fundamental Forces All other forces can be explained in terms of these fundamental forces 1. Strong nuclear force.

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Unit 5 - Fields Chapter 14 Chapter 15

Fundamental Forces All other forces can be explained in terms of these fundamental forces 1. Strong nuclear force 2. Electromagnetic force 3. Weak nuclear force 4. Gravitational force Increasing strength

Fundamental Forces All other forces can be explained in terms of these fundamental forces 1. Strong nuclear force (SNF)  Keeps the protons in the nuclei from repelling one another and disintegrating the atom.

Fundamental Forces All other forces can be explained in terms of these fundamental forces 2. Electromagnetic force  Long range force that is responsible for binding of atoms and molecules (the subject of this unit)

Fundamental Forces All other forces can be explained in terms of these fundamental forces 3. Weak nuclear force (WNF)  Governs stability of basic particles (quarks, leptons)  Closely linked to #2 (Electroweak theory)  About 10 6 times weaker than SNF

Fundamental Forces All other forces can be explained in terms of these fundamental forces 4. Gravitational force  Requires large objects, and close distances to be significant in size

Charge model Law of conservation of electric charge: charge can neither be created nor destroyed

Coulomb’s Law Used a torsion balance in 1785 (similar to Cavendish) Charles Augustin Coulomb (1736 – 1806)

Coulomb’s Law Only applies to point charges (no volumes) k = electrostatic constant = 9.0 x 10 9 N m 2 / C 2 q 1 and q 2 = charges of the two particles (in C) r = distance between the two particles An inverse- square law!

Coulomb’s Law Example 1, a small plastic sphere is charged to –10nC. It is held 1.0cm above a small glass bead at rest on a table. The glass bead has a mass of 15mg and a charge of +10nC. Will the glass bead “leap up” to the plastic sphere?

Coulomb’s Law Example 2, two charged particles, +5nC and +10nC, are 5.0cm apart on the x-axis.  What is the net force on a +1.0nC charge midway between them?  What is the net force if the charged particle on the right is replaced by a –10nC charge?  Where would a charge need to be placed between +1C and +4C charges that are 10cm apart in order to experience a net force of 0?

A word on magnetic force…  Magnetic monopoles do not exist: where there is an N, there is an S.  Very long, thin magnets can simulate this, and Coulomb found:

Fields So far, we’ve seen Coulomb’s law from a strictly Newtonion (classical) view. Newton’s law of universal gravitation also describes an action at a distance, but provides no mechanism

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers. —Isaac Newton, Letters to Bentley, 1692/3

Fields Questions that arose during (and after) Newton:  If particle A and B are attracted to one another, and A moves, how long does it take B to react? Is it instant? Speed of light? Faster than the speed of light?  What if A and B are light years away? A A B B

Fields Michael Faraday (1791 – 1867) was a brilliant physicist, but a poor mathematician. The behavior of iron filings around a magnet sparked his scientific interest

Fields In Faraday’s view (1849), object A alters or modifies the space around it, and object B then comes along and interacts with this altered space (creates a field ) A A B B

Fields Test charge (q t ): point charge with a magnitude much smaller than the source charge Electric Field Intensity (E): Measured in N/C qsqs qsqs qtqt qtqt

Fields E is a vector quantity! By convention, the direction of the electric field vector at any point is given by the direction of the force that would be exerted on a positive charge located at that point.

Fields E is a vector quantity!

Fields Example, a source charge creates an electric field. A +1.0nC test charge is placed in the field and experiences a force of 3.0 mN [W]. Sketch a possible scenario. What is the electric field intensity at the location of the test charge?

Fields Remember: A field is a property of space This same concept, when applied to Newton’s concept of gravitation, implies that all objects with mass create a gravitational field around them.

Fields Gravitational field intensity (g). All forces point inwards (towards the massive object)

Fields Another definition for electric field intensity: And gravitational field intensity (g): The strength of an electric field (E) at a distance (r) away from a point charge (q s ) is given by:

Field Lines Electric field lines - the vector sum of electric field vectors - recall the convention is to use a positive test charge as a reference

Field Lines Electric field lines with two charges: Like charges Unlike charges

Field Lines Gravitational field lines - always point inwards towards the massive object (much simpler)

Field Lines Magnetic field lines - magnetic monopoles do not exist!

Electrical Potential Two point charges, separated by a distance, r, have an electrical potential energy defined by: + + - - r

Electrical Potential Example, two point charges of +5nC and - 3nC are separated by 35cm. What is the electrical potential between the two charges? + + - - r

Electrical Potential

Electrical Potential (V)

Electrical Potential Electrical Potential Difference Electrical Potential

Electrical Potential Example, the work done on a test charge (q t = +2.0 x 10 -6 C) as it moves in an electric field from point A to point B is +5.0 x 10 -5 J. Find the value of the difference in the electric potential energies of the charge between these points Determine the potential difference between these two points.

Electrical Potential Example, three points (A, B, C) are located along a line. A positive test charge is released from rest at point A and accelerates towards point B. Upon reaching B, it continues to accelerate to point C. What will a negative test charge do when released from point B?

Electrical Potential Example, determine the amount by which a point charge of 4.0 x 10 -8 C alters the electric potential at a spot 1.2m away when the charge is (a) positive and (b) negative)

Conductors vs Insulators Conductors conduct electricity (usually metals) Insulators do not conduct electricity (non-metals)

Voltaic Pile Allesandro Volta created the first electrochemical battery (called the voltaic pile ) by using alternating disks of silver and zinc:

Battery basics Electrode : cathode (gains e - ) or anode (gives e - ) Electrolyte : material through which the e - flow

Intro to circuits Two requirements for a working circuit: 1. Energy supply (battery) long line = + (cathode) short line = - (anode)

Intro to circuits Two requirements for a working circuit: 2. Closed loop

Electric Current Electric current ( I ) is the amount of electric charge that passes through a point in a circuit per unit time. 1 ampere (A) = 1 coulomb per second (1A = 1C/s)

Electric Current Electric current ( I ) is the amount of electric charge that passes through a point in a circuit per unit time. 1 ampere (A) = 1 coulomb per second (1A = 1C/s) +- cathodeanode electric current electron flow

Electric Current Example, in the cross-section of a wire below, 10C of charge pass through a 50-cm region in 2.0s. What is the current in the wire?

Elementary Charge In 1897, JJ Thomson discovered the electron. From his measurements, he was able to estimate the charge:mass ratio.

Elementary Charge In 1917, Robert Millikan’s oil drop experiment showed that when electrons moved, they moved in whole- number amounts.

Elementary Charge He estimated that each individual electron possesses a charge of 1.60 x 10 -19 C, now called an elementary charge (e)

Elementary Charge Total charge (in C) Number of e - (whole number) Elementary charge

Resistance and resistivity Similar to friction, a certain level of resistance ( R ) exists in all real situations. A high resistance means the material impedes the flow of electrons. Measured in ohms (Ω, omega)

Resistance and resistivity Longer, thicker wires have more resistance Resistance is related to these quantities by a proportionality constant called resistivity (ρ, rho), which varies depending on the electronic structure of the substance and the temperature

Ohm’s law An empirical law for conductors, which states that the voltage is proportional to the current Devices that follow ohm’s law are said to be ohmic (we will not deal with non-ohmic devices)

More on circuit diagrams Things that drop the electric potential in a circuit are known as loads or resistors. These may be lights, heating elements, etc… or = Resistors cause potential drops in a circuit, while a battery restores the potential of electrons.

More on circuit diagrams Example, in one minute, how many electrons pass through any point in a circuit composed of a 1.5V battery and a light bulb with a resistance of 3Ω? Sketch the circuit.

Series vs parallel circuits For resistors placed in series, all of the current flows through all of the loads/resistors, with the potential dropping after each one. If one of the loads/resistors is blocked, all loads turn off

Series vs parallel circuits

For resistors placed in parallel, some electrons flow through each route and re-group to return to the battery.

Series vs parallel circuits

Voltmeters and Ammeters Voltmeters must be placed in parallel to measure the voltage drop across a region of a circuit. Voltmeters must have a high resistance to ensure that electrons do not flow through it (electrons will travel through the path of least resistance)

Voltmeters and Ammeters Ammeters must be placed in series, and measure the amount of electrons passing through it. Ammeters must have a low resistance in order to not interfere with the flow (current) of electrons.

Kirchoff’s laws Kirchoff’s laws: 1.Kirchoff’s junction rule The sum of currents flowing into a junction is equal to the sum of currents flowing out of that junction.

Kirchoff’s laws Kirchoff’s laws: 2. Kirchoff’s loop rule In any closed loop, the total voltage around the loop is equal to the sum of the voltage drops within the same loop

Internal Resistance & EMF All real batteries contain some internal resistance (V int ) due to the components that make it up. The electromotive force, or emf, is the theoretical voltage of a battery, assuming no current passes through it. The potential difference, as measured across the electrodes is called the terminal voltage (V s ).

Power revisited Combining this with Ohm’s law, we can also see: Combine the equations for power and potential:

Power revisited Kilowatt hours (kWh) -A common way to measure energy -Equivalent to 3.6MJ:

Power revisited Example, a label on a kettle says it has a wattage of 1800W. If energy costs 0.15USD per kWh, how much money does it cost to run the kettle for 1 hour per month?

*E = V

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