CONCEPTUAL PHYSICS: UNIT 5

Electricity and Magnetism

SP5. Students will evaluate relationships between electrical and magnetic forces.

a. Describe the transformation of mechanical energy into electrical energy and the

transmission of electrical energy.

b. Determine the relationship among potential difference, current, and resistance in

a direct current circuit.

c. Determine equivalent resistances in series and parallel circuits.

d. Determine the relationship between moving electric charges and magnetic fields.

Part 1: Elements and Charges

An element is the purest form of matter. All elements are composed of one type of

atom. An atom is the smallest unit of matter that defines an element and retains the

chemical and physical properties of that element. Elements are classified by their

chemical behavior, physical and chemical properties, and chemical reactivity. Elements

can be divided into three generic categories: metals, metalloids, and non-metals. The

elements belonging to each group are shown in the Periodic Table of the Elements below.

The one or two letters that represent elements are called the chemical symbol. The

number in the upper left corner of each element’s square is the atomic number.

Periodic Table of the Elements

Metals are on the left and center region of the Periodic Table of the Elements. Metallic

elements have a metallic luster, tend to be silvery in color, chemically-react to form

cations, and conduct heat and/or electricity. Non-metal elements are on the upper right

side of the Periodic Table of the Elements. Non-metals tend to be gases or solids that do

not have metallic lusters, do no conduct heat or electricity, and chemically-react to form

anions. Semiconductor elements, sometimes called metalloid elements, have some

properties that are like metals and some that are like non-metals. Semiconductors, or

“half-conductors”, have a moderate ability to conduct electricity.

The atom is the smallest unit of matter that defines and maintains the chemical properties

of elements. Atoms are composed of the subatomic particles protons, neutrons, and

electrons. The nucleus is the dense core of the atom, composed of the protons and

neutrons that are tightly bound to each other. Electrons, compared to protons and

neutrons, are very tiny. Electrons move freely in the 3-dimensional space around the

nucleus of the atom. The diagram on the next page shows the structure of a single

carbon atom.

Protons and neutrons are the subatomic particles in the nucleus of the atom. Protons

have a positive charge, indicated by the + sign. Neutrons are neutral, they have no

charge. Protons and neutrons are held together very tightly in the nucleus of the atom by

the atomic strong force. The atomic strong force is millions of times stronger than

gravity. Conversely, electrons have a negative charge, indicated by the – sign. In short,

the nucleus of the atom has a positive charge because of all of the protons and the space

around the atoms has a negative charge because of all of the electrons. The electrons are

attracted to the nucleus by electrostatic force. Objects with positive charges are attracted

to objects with negative charges.

Electrons move very fast in the space

around the nucleus of the atom. Some

electrons are closer to the nucleus, some

electrons are farther from the nucleus. The

electrons that lie the farthest distance from

the nucleus are called valence electrons.

Valence electrons are important because

they control the chemical properties and

reactivity of elements, as well as the

conductivity electricity by elements.

Atoms and Ions The valence electrons are the electrons that cause chemical reactions and allow for

electrical currents to be conducted through metals. During chemical reactions, atoms

interact by taking and giving valence electrons. Non-metal atoms will take valence

electrons away from metal atoms. Electrons always move, never protons or neutrons.

When atoms have equal numbers of protons and electrons, the atoms are electrically

neutral—the number of positive subatomic particles equals the number of negative

subatomic particles. After a chemical reaction, electrons are taken away from some

atoms and gained by other atoms. In that case, the atoms are no longer neutral. The

atoms are now charged with a negative or positive charge. These are called ions. An ion

is an atom that has an electric charge because it has lost or gained valence electrons.

If an atom has 1 or more valence electrons taken away from it by another atom, that atom

will have more protons than electrons, thus have a positive charge. Ions with positive

charges are called cations. Metals atoms have electrons taken away from them during

chemical reactions and form cations. If an atom has 1 or more valence electrons gained

by taking electrons from another atom, that atom will have more electrons that protons,

thus have a negative charge. Ions with negative charges are called anions. Non-metal

atoms take away electrons from other atoms during chemical reactions and form anions.

Positive charged particles (like the +1 Na cation) attract negative charged particles (like

the -1 Cl anion). When there are billions and billions of these cations and anions together

moving around in water, they form electrolytes. Electrolytes are cations and anions that

conduct electricity when dissolved in water. The more electrolytes that are dissolved in

water, the easier it is for electricity to pass through the water like a circuit. Electrons in

the electricity will jump from cation to anion to cation to anion through the water.

The diagram shows a sodium atom (Na)

chemically reacting with a chlorine atom

(Cl). Sodium is a metal. Chlorine is a non-

metal. During the chemical reaction, the

chlorine atom takes one valence electron

away from the sodium atom. When the

chemical reaction is complete, the chlorine

atom has a -1 charge because it has one

electron more than protons (17 protons and

18 electrons). The sodium atom has a +1

charge one electron fewer than protons (11

protons, 10 electrons).

This is important because living organisms need electrolytes in the cytoplasm of cells,

blood, sinovial fluid, and in the fluids between nerve cells to transmit electric impulses to

nerves, muscles, cellular organelles, etc…

Metallic Bonding and Electrical Conductivity

Conductive Metals

1. Silver

2. Copper

3. Gold

4. Aluminum

5. Zinc

6. Nickel

7. Brass

8. Bronze

9. Iron

10. Platinum

The atoms of pure metals, like gold, copper, silver, and lead are very small, dense, and

packed together very tightly. When the atoms of metallic elements are packed together

very tightly, they will interact with each other by metallic bonding. Metallic bonding

occurs when the valence electrons of all of the tightly packed atoms begin to flow from

one atom to the neighboring atoms. In the diagram, the valence electrons are moving

from atom to atom—they are not held around one single atom.

Metallic bonding increases conductivity of electricity. Copper is an excellent conductor

of electricity because of metallic bonding. When copper metal is twinned into wire,

copper will conduct electricity. The electrons from the electrical source will very easily

flow through the wire because the valence electrons already present in the wire are freely

moving.

Part 2: Law of Charges, Coulomb’s Law, and Electric Fields

Objects that are charged (have positive and/or negative charges) interact according to the

Law of Charges and Coulomb’s Law. Law of Charges and Coulomb’s law describe how

charged objects interact with each other and how much force they apply upon each other.

Law of Charges: Opposite charges attract each other, alike charges repel each other.

Positive charges attract negative charges.

Positive charges repel positive charges

Negative charges repel negative charges

Coulomb’s Law: The mutual attractive or repulsive electrostatic force between two

charged objects is proportional to the magnitude of the charges and inversely proportional

to the distance between the objects.

The greater the charges, the greater the attraction force and/or repulsion force between

the objects.

The lesser the charges, the lesser the attraction force and/or repulsion force between the

objects.

The shorter the distance between the charged objects, the strong the attraction and/or

repulsion between objects.

The greater the distance between the charged objects, the weaker the attraction and/or

repulsion between objects.

Law of Charges The atoms in positive-charged objects have fewer electrons than protons. The atoms in

negative-charged objects have more electrons than protons. According to the Law of

Charges, the positive-charged objects attract negative-charged objects. In the absence of

other forces, + will attract -. Opposite charged particles want to pull each other closer.

Conversely, objects with the same charge (positive to positive, or negative to negative)

repel each other. In the absence of other forces, two objects with the same charge will

push away each other. This is the result of electric fields (or electric forces) that

surround charged objects. The figure below shows the electric fields (illustrated by the

lines) that surround objects with charges. Electric field lines cannot touch each other or

overlap, they may only move out of positive-charged objects and flow into negative-

charged objects.

Electric fields (force) move outward and away from positive-charged objects. Note that

the arrows of the lines are pointing away from the (+) object. Electric fields (force) move

toward and into negative-charged objects. Note that the arrows of the lines are pointing

toward the (-) object. The diagram on the left shows a positive-charged object

interacting with a negative charged object. Electric fields move out of the (+) object and

flow into the (-) object. This is why opposite charged objects attract. The diagram on the

right shows two positive-charged objects interacting. Electric fields are moving out of

both (+) objects, thus the fields moving outward cause both to repel each other.

Coulomb’s Law Coulombs Law describes the attraction or repulsion force between charged objects. In

short, the greater the charge and the closer together the charged objects are to each other,

the stronger the attraction or repulsion force. Coulomb’s Law describes mutual attraction

or mutual repulsion—each object attracts or repels the other object with equal and

opposite force (obeys Newton’s 3rd

Law of Motion).

2

21

d

qqkF

q1 = the net charge on object or point charge 1 (Coulombs)

q2 = the net charge on object or point charge 2 (Coulombs)

d = distance between the charged objects or point charges (m)

k = Coulomb’s constant

The variables q are the charges of the objects in Coulombs (the unit of charge). The

constant k is Coulomb’s constant. The constant k is a very large number, 2

291000.9

C

mN ,

which is approximately a billion billion times greater than Newton’s Universal

Gravitation Constant, G. In other words, electrostatic attraction and repulsion is much,

much, much stronger than gravity. Note that the distance, d, is squared and in the

denominator. The strength of the electric field and by consequence the strength of the

attraction/repulsion force decreases that farther the objects are apart. If you look at the

diagrams, notice that the electric field lines are very close together when close to the

charged objects. The electric field lines become farther and farther apart with increasing

distance away from the charged objects. When objects are closer together, they pull or

push with more force on each other. When objects are father apart, they pull or push with

lesser force on each other.

Part 3: Static Electricity

Electricity is caused by electrons. Sometimes electrons flow through conductive

materials, such as metallic wires and concentrated electrolyte solutions. In this case, the

electricity has an electrical current. Current is the rate at which charges (e.g., electrons)

move through a conductive material. In other cases, electricity is stored or is stationary

on objects-not moving. Static electricity (sometimes called static charge) occurs when an

electrical charge (positive and negative) is stationary on the surface of objects. The static

charge will remain on the surface of objects until it is discharged—electrons jump from

the electron-rich (negative) surface to a conductive material (metal) or to a positive

surface. Static electricity or static charge can accumulate on surfaces by friction or

induction.

The creation of static charge by friction occurs when two

objects, one usually made of an insulating material

(rubber, plastic, glass) is vigorously rubbed or moved

against another object. The insulator will strip electrons

away from the atoms on the surface of the other object.

In the example to the right, the girl combs her hair with a

rubber comb. Before she combs her hair, the comb and

the hair have neutral charge. Rubber is an insulator. As

she combs her hair, the comb strips electrons from some

of the atoms in her hair. The comb accumulates a static

negative charge. Her hair accumulates a static positive

charge. Both the comb and her hair will have the static

charge until discharge. Note that her hair will stick up

and frizz when the comb is brought near because negative

(comb) will attract the positive (hair).

The same effect can be achieved by rubbing a rubber balloon against your hair or against

fabric. Another way is to rub your shoes across shag carpet. The rubber in the balloon or

bottom of shoes will strip electrons off of the atoms in the hair, fabric or carpet. The

rubber will accumulate a static negative charge, the hair and fabrics will accumulate a

static positive charge. Lightning is the violent discharge of static electricity from

negative-charged clouds and positive-charged clouds.

The creation of static charge by induction

occurs when an electrically charged object is

brought very close to another object that is

initially neutral. The charge on the surface of

the first object causes the electrons on atoms on

the surface of the second object to shift and

reorient themselves so that the opposite charge is

on the surface. A charged object induces the

opposite charge on the surface of another object.

In the example, normal paper is neutral. The

electrons are distributed around their respective

atoms normally. When the negative-charged comb is brought close to the paper, the

electrons around the atoms on the paper shift and point away from the comb—negative

charged electrons want to face away because same charges repel. Because the electrons

face away, the nuclei of the atoms (with the positive-charged protons) are now facing

toward the comb because opposites attract. When the comb is brought very close to the

paper, the paper will begin to move toward the comb because of the attractive force

between positive and negative charged objects.

Part 4: Properties of Series and Parallel Circuits

Circuits are connections that are made between power sources and appliances through

electrically conductive materials. Closed circuits are those that have a connection and

allow for electricity (moving electrons) to move uninterrupted. Open circuits or broken

circuits are those that do not have a connection and do not allow for electricity to move.

Electricity can only flow through closed circuits. Electricity will always flow through the

“path of least resistance”. Electricity will try to move through the wire that has the fewest

resistors. Short circuits arise when electricity avoids the main circuit by passing through

a piece of metal or another wire that has no resistance. Some circuits have switches,

which purposefully open and close circuits. “On-off” buttons are switches, they contain

wire or cable to complete the circuit when “on” and break/open the circuit when “off”.

Fuses are small metallic disks that will open or break a circuit if too much current passes

through the circuit. Fuses protect the device from overheating and perhaps bursting into

flames if the circuit becomes too hot due to too much current.

Series Circuits

Series circuits are circuits in which the power supplies (batteries or generators) or the

resistors (appliances, devices that use electricity to perform work) are arranged in a linear

order on the same circuit or power wire.

Power supplies in series: Notice that the batteries are

arranged in a linear order on the same circuit. When

power supplies are in series, the total electric potential

across the circuit is the sum of the voltages. Add the

voltages for all of the

power supplies together. Potential is reported in units of volts (V).

Calculate the voltage with series power supplies

nseries VVVVV ...321

Resistors in series: Notice that the appliances (the

circles) are arranged in a linear order on the same circuit.

When resistors are in series, the total resistance across the

circuit is the sum of the resistances. Add the resistances

for all of the appliances together. Resistance is reported

in units of Ohms (Ω).

Calculate the resistance on series circuits

nseries RRRRR ...321

+

-

+

-

+

-

+

-

Parallel Circuits

Parallel circuits are circuits in which the power supplies or the resistors are arranged on

individual branching wires connected to the main circuit.

Power supplies in parallel: Notice that the batteries are

arranged in parallel, each has its own wire connected to

the main circuit. There is also one appliance (the circle).

When power supplies are in parallel, the total electric

potential across the circuit is equal to the battery with the

greatest voltage. If there many batteries with different

voltages, the voltage is equal to the greatest.

maxVVParallel

Resistors in parallel: Notice that the appliances (the

circles) are arranged in parallel, each has its own wire

connected to the main circuit. There is also one battery.

When resistors or appliances are in parallel, the total

resistance across the main circuit is calculated as follows:

Step 1: Add together the reciprocals of the resistances (see below)

Step 2: Flip the fraction answer from step 1 and simplify if necessary.

nRRRRR

n 1...

111

321

ParallelRn

R

R

n

Charge

Charge (q) is the positive or negative electrical energy attributed to a charged surface or

particle. Charge is reported in units of Coulombs. The quantity of charge attributed to

the surface of an object or on a particle is directly related to how many extra electrons the

surface or particle has accumulated (for negative-charged objects) or the number of

electrons lost by a surface or particle (for positive-charged objects).

The charge of 1 electron is q = - 1.61x10-19

C

electrons have a negative charge, hence q is negative.

The charge of 1 proton is q = +1.61x10-19

C

protons have a positive charge, hence, q is positive.

Electric Potential (Voltage)

Voltage (V) is the electric potential established by the power supply. Voltage defines the

amount of work that can be performed by moving electrons from the power supply

(source of electrons and electricity) to its destination. When a circuit is created, the

power supply first creates the electric field (the electric force) that will push the electrons

through the circuit. Electrons flow through the circuit because of the electric field.

When the electricity passes through resistors or appliances, electric energy is transformed

into work. The voltage across the entire circuit always remains constant.

The greater the voltage, the greater the electric potential, the stronger the electric field

across the circuit, the more work can be performed by electricity.

The lesser the voltage, the lesser the electric potential, the weaker the electric field

across the circuit, the less work can be performed by electricity.

Resistance

Resistance (R) is the reduction or the resistance of a circuit to allow electricity to flow

through it. Resistance is created by resistors or appliances on the circuit. An appliance

is any device that is transforming electrical energy to work (e.g., light bulb, toaster,

heater). The more resistors or appliances that are added in series to the circuit greatly

reduce the flow of electricity—the current decreases. For example, if you use your

toaster, you may notice that lights in the kitchen dim. This indicates that the toaster when

in use has slowed the flow of electricity in your kitchen’s wiring. Then the toaster pops

the toast, the lights in the kitchen brighten. The resistance of the toaster is now zero

because it is not turned on, and the flow of electricity became faster through your

kitchen’s wiring. In addition to the transformation of electrical energy to work, resistors

always produce wasted energy in the form of heat.

Most modern wiring of households arranges outlets and large appliances on parallel

circuits rather than series circuits. This is done for two reasons. First, when each

appliance is on its own circuit rather than a common circuit, the change in resistance and

power usage does not affect greatly the other appliances. Second, if appliances were in

series, if one appliance shorts, the others on that series circuit would not function because

the circuit will be broken or open.

The greater the resistance, the more electrical energy being converted to work and heat,

the slower the electricity will flow through the circuit.

The lesser the resistance, the lesser the electrical energy being converted to work and

heat, the faster electricity will flow through the circuit.

Other considerations for resistance in circuits

MORE RESISTANCE LESS RESISTANCE

Wire thickness Thinner wires Thicker wires

Temperature Hotter wires Colder wires

Wire length Longer wires Shorter wires

Materials Insulators/Semiconductors Metals/Conductors

Current (I)

Electrical current is the rate of movement of charge through a circuit. Current is reported

in units of Amperes (Amps), and is C/s. According to Ohm’s Law, the current of a

circuit is proportional to the voltage of the power supply and inversely proportional to the

resistance of the circuit. The equation below represents Ohm’s Law, the product of

current and resistance is voltage.

RIV

When Ohm’s law equation is rearranged, the current across the circuit can be calculated.

R

VI

Current is the rate (how fast) charge moves through a wire. According to Ohm’s Law,

the following is true.

The effect of voltage

The greater the voltage of the power supply, the greater the electric field, the more

forceful electrons are pushed through the circuit, the greater the current.

The lesser the voltage of the power supply, the lesser the electric field, the less forceful

electrons are pushed through the circuit, the lesser the current.

The effect of resistance

The greater the resistance on the circuit, the lesser the current.

The lesser the resistance on the circuit, the greater the current.

How current affects appliances

The greater the current, faster energy passes through the appliance, the greater the

power (work per second) performed.

The lesser the current, slower energy passes through the appliance, the lesser the power

(work per second) performed.

Part 5: Magnets

Magnets are metallic materials that generate magnetic fields, forces that attract or repel

other magnetic materials. Magnetic metals include iron, nickel, and neodymium.

Magnetism is a fundamental force, like gravity, and is related to electronic (electrons)

and charge distribution in metallic elements. Magnetism and magnetic fields can

generate electric fields and electricity. Likewise electricity and electric fields can

generate magnetic fields and magnetism.

Each magnet has two defined terminals, or dipolar: north pole and south pole. The

north pole is defined as the pole where the magnetic field emerges from the magnet. The

south pole is defined as the pole where the magnetic field returns to the magnet. The

magnetic field is drawn as a series of lines, however, the magnetic field is invisible. The

arrows show the direction of the force of the magnetic field around a bar magnet and

horseshoe magnet. The orientation of the north and south poles of magnets are

determined by using a compass or series of compasses. Compass needles align with the

direction of the magnetic field motion—the arrow points in the direction moving from

north pole to south pole. Earth has a strong magnetic field, generated by the motion of

the Earth’s molten outer core. Technically, the Earth’s north magnetic pole is actually

the south pole of the “Earth magnet” system. Additionally, the strength of the electric

field decreases with increasing distance away from the poles of the magnet. The farther

away from the north or south pole of the magnet, the weaker the magnetic field force.

Law of Poles. The law of poles is very similar to the law of charges. The law of poles

states that opposite poles of magnets attract, the same poles of magnets repel.

North and south poles of two different magnets attract.

North and north poles of two different magnets repel. South and south poles of two

different magnets repel.

The law of poles is true for similar reasons why the law of charges is true. The magnetic

fields (force) produced by magnets are unidirectional. Magnetic fields emerge from the

north pole of magnets and flow into the south pole of magnets, the pass though the

magnet to emerge again. Notice that when two like poles face each other (in this case

north and north), the magnetic fields will repel each other because fields cannot overlap.

The fields on both magnets are emerging. The same would happen if south faced south,

the fields cannot overlap and the fields on both magnets are returning to its respective

magnet. When opposite poles of two different magnets attract and come together, they

form one large continuous magnet. Conversely, if bar magnets are broken or cut into

smaller segments, each segment will generate a north and south pole.

Magnets have the ability to induce magnetism in paramagnetic metals. For example,

paper clips and nails are made of stainless steel, a composite metal with iron. Some

forms of iron and stainless steel are not naturally magnetic—they do not on their own

attract other metallic objects and do not generate their own magnetic fields.

When paramagnetic objects come into contact with magnets, the

magnetic fields will pass through them such that those objects become

extensions of the magnet. In other words, the magnet will induce

magnetism through those objects. That is why magnets will stick to

iron-containing objects or pick up small steel objects.

Part 6: Power Supplies and Electromagnetism Power supplies are devices that create electrical energy from different sources. The most

familiar power supply is the dry cell battery. Batteries convert chemical energy into

electrical energy. The battery will have two chambers with two different ionic

compounds separated by a membrane. When the two electrodes of the battery are

connected by a wire, electrons will flow from the compound in the anode chamber to the

compound in the cathode chamber.. The anode is the negative terminal of the battery—

the source of electrons; the cathode is the positive terminal of the battery—the

destination of electrons. Batteries will always produce direct current.

A generator is a device that converts mechanical energy (KE) into electrical energy.

This is how most electrical energy at power stations is created. Inside the mechanics of

the generator, kinetic energy from an outside source, like flowing water, blowing wind,

or fast moving steam, causes turbines to rotate at very high speeds. This rotational KE is

converted by dynamos to mechanical energy. The mechanical energy moves magnets

inside copper coils and generates electricity by electromagnetism. Conversely, electric

motors convert electrical energy to mechanical energy that allows for the device to

perform work.

Electromagnetism is the ability of magnetic fields to generate electricity and for

electricity to generate magnetic fields. Electromagnetism is the process by which

electricity in most commercial power plants is generated.

Electrical current can produce a

magnetic field. As electricity flows

through a circuit, the moving electrons

in the electric field will create a

perpendicular magnetic field with a

force direction clockwise to the wire.

The strength of the magnetic field decreases with increasing distance from the wire. A

stronger dipolar magnetic field is created by coiled copper wire. When wires are coiled,

the magnetic fields from each segment of the wire align, strengthening the magnetic field

and giving the force a defined N and S direction. If a tightly-wound copper coil has a

very high voltage and very high current passing through it, that coil will generate a very

strong magnetic field—this type of device is called an electromagnet.

Conversely, large permanent magnets can produce electric fields which in turn can

produce electrical current. All commercially-generated electricity in the US and other

countries is alternating current (AC). AC is created when large magnets in the

generators of power plants rotate very high speed inside a tightly-wound coil of

copper—or a tightly-wound coil of copper rates inside a large magnent. As the magnet

spins or coil of copper spins, the N and S poles of the magnet take turns facing the

coil.The alternating direction of the magnetic field (outward by the N, inward by the S)

will create an alternating electric field.

At one instant, the electrons are

pushed away from the magnet. At

another instant, the electrons are

pulled toward the magnet. The other

type of current is direct current (DC)

in which electrons are pushed through

a wire in only one direction. DC

current is usually generated by

batteries.