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Electricity and Magnetism: Study Guide
I. Basics
A. Based on charge of particles (p+ and e-)
B. Charges
1. Measured in Coulombs (c)
2. Coulomb based on charge of 1 ea. e- = 1.6022 x 10-19 c
b. 1 c = 6.242 x 1018 eC. Law of Electrostatics – likes repel, opposites attract
D. Law of Conservation of Charge
E. Current
1. DC – Direct Current
2. AC – Alternating Current – direction of e- flow reverses 60 x per second
a. Standard in U.S. is 120 V at 60 Hz
II. Charging of Objects
A. Friction
B. Conduction - contact
C. Induction – no contact, through field
III. Electric Fields and Charges
A. Electric force between two objects depends on charge and distance
B. F = k x Q1 Q2 / d2 where k is constant of 8.988 x 109 Nm2/c2; Q1 and Q2 are charges and
d is distance between objects
1. K = 1 / 4 π ∈ 𝑜 where ∈ 𝑜 is the electric permittivity of free space and is equal to
8.854 187 82 x 10-12 F/m
C. Coulomb’s Law
1. 1 coulomb = ampere
a. Amount of charge flowing through a wire in 1 second with a charge
of 1 ampere
2. 1 amp = 1 c/sec
D. Electric Current (I)
1. Movement of electric charges
a. Measured in amperes
2. Intensity of current is amps (c/s)
3. Current (I) = Charge (Q) / Time (t)
E. Electric Potential (V)
1. Measured in volts
2. Volt is stored electrical PE
3. Difference is between + and – terminals
a. Amount of work in an electric field to take one coulomb from one
point to another
4. Voltage related to work
a. V = Work (W) / Q (Charge)
b. V = 1 Joule / Coulomb
c. V x amp = Watt (power)
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F. Resistance (R)
1. All materials absorb/divert/repel some e- flow
2. Resistance measured in ohms (Ω)
3. R = p x L/A where p is density constant for material, L is length and A
is surface or end area (𝐴 = 𝜋𝑟 2 )
4. Ohm’s Law (Ω)
a. V = I x R (Voltage = Current in Amps x Resistance in Ohms)
b. R = V / I
5. Resistance in Series
a. R1 + R2 + R3 + …. = RTotal
6. Resistance in Parallel
a. 1/R1 + 1/R2 + 1/R3 + …. = 1/RTotal
7. Opposite is Capacitance which stores e-‘s and releases flow at certain level
a. Made with two conducting plates separated by an insulator
called a dielectric
a. C = Q / V
b. Measured in farads (1 coulomb per volt)
c. Parallel Capacitance
a. C1 + C2 + C3 + … = CTotal
d. Series Capacitance
a. 1/C1 + 1/C2 + 1/C3 + … = 1/CTotal
e. C = ∈ A / d
a. C is capacitance in farads; ∈ is constant = 8.8562 x 10-12 F/m; A is
plate area in m2; and d is distance between plates
G. Electrical Power and Work
1. P = V x I
a. In Watts (J/s)
b. P = V2 / R ; P = I2 x R;
P = VxI
2. Work (WE) = q V
a. In Joules
F. Electric PE
1. PE = K q Q / R
a. V = PE / Q
IV. Batteries
A. Works through electrochemical reactions
B. Anode (+) and Cathode (-) in acid which is an electrolyte
1. e- flow from cathode to anode and out + terminal
2. Usually are Zn and Cu in H2SO4
C. Historical Batteries
1. Baghdad Battery
2. Voltaic Pile layers of Cu and Zn discs with NaCl water as conductor
3. Daniel Cell
4. Lead Acid Battery
5. Gravity Cell
6. Dry Cell
D. Thermocouple – uses heat differences between two metals to produce charge
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Magnetism
I. Sources
A. Due to electrical charge
1. Magnetism and electricity part of same force (EMF)
2. These two fields run parallel to each other, and one produces the other
and vice versa
3. Magnetism similar to electricity – have +/- and opposites attract, likes repel
B. Magnetism also due to behavior of atoms and subparticles
1. Derives from e- orbitals, spin and angular momentum
a. Usually – e- behaviors cancel each other out to make atom neutral,
but when don’t, get magnetic charge
b. Called the intrinsic magnetic moment or the dipole moment
c. When dipole moments align – end up with magnetic domain
d. When domains align – material becomes magnetic
2. All magnets have 2 poles – No such thing as monopole
II. Types of Magnetism
A. Diamagnetism
1. No unpaired e-‘s (all spins matched so they cancel each other out)
2. No dipole moments, no domains, no magnetism
B. Paramagnetism
1. Material has some unpaired e-‘s
2. Creates some dipoles and domains – but only align and become magnetic
in presence of another magnetic field
a. When external field removed – material becomes non-magnetic again
b. Soft magnet – easily magnetized but does not stay so
C. Ferromagnetism
1. In metals – the lattice structure of atoms creates e- sea model
a. Delocalized e-‘s that can move from one atom to another
2. e-‘s gain same spin, remain in a parallel orientation
3. Creates domains and permanent dipole moment
a. Ferromagnets stay magnetic
b. Hard magnets – difficult to magnetize but remain this way
(1) Ni, Co, Fe
4. Will lose magnetism if material heated above Curie Temperature
a. This high temp causes KE of atoms to mess up spins, domains and field
III. Magnetic Fields and Force
A. Magnetism is a field force
1. Occurs at same time and parallel to electric field
a. Found by Hans Christian Oersted in 1820
2. No contact needed for effect of force
a. 2 fields – B and H
b. F = q (V x B) where q is charge, v is velocity of particle, and
B is magnetic field measured in Teslas
(1) Earth’s Magnetic Field is 0.0001 T
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(2) Tesla = N / (c x m/s) = N / (A x m) = (v x s) / m2
c. James Clerk Maxwell – EMF equations
d. Field Lines called Faraday Lines – used to visualize field force
B. Right-Hand Rule for magnetic and electrical fields
C. Solenoid
1. Concentrates magnetic field
2. If wrapped around iron, create electromagnet
3. Increase electric current – increase magnetic field
4. Found by Ampere
Summary:
Magnitude of Charge
 Coulomb’s Law
 FElectric = K q q’
r2
 K = 8.988 x 109 Nm2/c2
 q and q’ are charges of objects
 r is distance between objects
Coulomb (c)
 Amount of charge flowing through a wire in 1 second with a current of 1 ampere
 Ampere is 1 Coulomb per second
 Based on the charge of an electron
 1 coulomb = 6.242 x 1018 eo Current (I) = Q / t in amperes
 Measuring the intensity of the electric current
o V = IR
o R = V/I
 Charge of an electron (e-) = 1.60218 x 10-19 c = 1 eV
Potential Difference (V)
 Amount of work in an electric field to take the charge of 1 coulomb from one point to
another
 Volt is the potential difference across a conductor that carries a current of 1 amp
 V = W/Q
o V is potential difference in Volts
 I volt = J/c
o W is work done in Joules
o Q is charge in Coulombs
 Electric Field = V / d
o E = F/q
o In Newtons / Coulomb
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Resistance (R)
 Measured in Ohms  Ω
 Resistivity = density (ρ) Length (L)
Area (A)
 R = V/I
o I ohm (Ω) = 1 V / Amp
 Ohm’s Law  V = I R
o Voltage = Current in Amps x Resistance in Ohms
 Resistance in Series
o R1 + R2 + R3 + …. = RTotal
 Resistance in Parallel
o 1/R1 + 1/R2 + 1/R3 + …. = 1/RTotal
Capacitance (C)
 C = Q/V
 Measured in farads (1 coulomb per volt)
 Parallel Capacitance
o C1 + C2 + C3 + … = CTotal
 Series Capacitance
o 1/C1 + 1/C2 + 1/C3 + … = 1/CTotal
 C = ∈A/d
o C is capacitance in farads; ∈ is constant = 8.8562 x 10-12 F/m; A is plate area in m2;
and d is distance between plates
Work and Power
 Work (WE) = q V
o In Joules
 Power (P) = V q / t
o In Watts (J/s)
o Power also = V I = I2 R = V2 / R
Electric PE
 In Joules
 PE = K q Q / R
o V = PE / Q
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