Fields - Electric Fields

examples of applications of electric and magnetic fields

• electrocardiogram

• photocopiers

• scrubbers that remove particulate matter

laws of electric charges

• oppo charges attract

• like charges repel

• charged obj’s attract some neutral obj’s

what is elec charge

• neutral atom

• cation (# of protons > electrons)

• anion (# of electrons > protons)

basic unit of elec charge

Coulomb (C)

• 1 C approx = amount of elec charge that passes through a 60 W light bulb in 2 s

watts (W)

methods of charging

• friction (depends on force of attraction b/w nucleus and its outer elections)

• induction (charged obj is brought close to a neutral obj WITHOUT contact)

• contact (charged obj makes contact w neutral obj)

law of conservation of charges

Charge can be created or destroyed but the total charge (the difference between the amounts of positive and negative charge) within an isolated system is always conserved.

• 1 object gains e- while another loses the same amount

pt charges

vv small particles that carry a charge

coulomb’s law

see formula for electric force

coulomb’s law related to newton’s 3rd law

the elec force exerted on charge A by charge B is the same in mag and oppo in dir than the force exerted on charge B by charge A

comparing coulomb’s law to newton’s law of grav force

• one is attractive and repulsive while the other is only attractive

• both forces are non-contact

• both forces act along a line joining the obj’s centers

• both have constants but G is vv small while K is vv large but is cancelled out by the small charges

Fe is much _____ than Fg

greater

for more than two pt charges

you must calculate the vector sum of the elec forces and find the net force

when does the coulomb law apply

when the 2 charges are vv small compared to their dist

force

a push or pull on an obj

field of force

exists in a region of space when an appropriate object placed at any point in the field experiences a force.

properties of elec fields

• a charge generates an elec field

• an elec field causes an elec force and is the spetial region in which a force is exerted on any elec charge

• field exerts attractive/repulsive forces on other charged obj’s

• elec field is a vector (epselon symbol)

elec field

the elec force per unit POSITIVE CHARGE (N/C) this is why a pos charge always emits an elec field while a neg charge seems to accept it

elec fields (cont’d)

• elec field lines always start on + charges and end on - charges

• lines nvr cross

• concentration of lines = strength of field

elec fields diagram

field theory

• as r increases, field strength decreases and Fe also decreases

• as r approaches infinity, field stren approaches 0 as well as Fe

Fe =

q (quantity affected by field) * epselon (field strength) (N/C)

Fg =

m (quantity affected by field) g (field stren) (N/kg)

epselon =

Fe/q OR kq/r² (the first works for charge distributions)

uniform elec fields

• epselon does not depend on the separation of the plates

• mag of elec field b/w 2 plates is directly proportional to the charge per unit area on the plates.

• 𝜀 is uniform everywhere in the space b/w the plates

when you pull or push a charge in the oppo dir of its tended path, you are

exerting a force over a distance thus doing work and thus converting kin to elec pot en

both grav and elec forces are

conservative

elec pot en is stored by

2 separated charges just as gravitational potential energy is stored by 2 separated masses but EE can be for charges that either attract or repel

see notes for formulas

when 2 charges are alike, work is done when

the charges are brought together, thus as r decreases, Ee increases and kin en decreases, so the Ee formula is positive

when 2 charges are opposite, work is done when

the charges are being separated, thus as r decreases, Ee decreases and Ek increases, if work is done to separate them, Ee becomes less negative as they are brought further apart

when work is done against the natural tendency of the charges

Ee increases since W = change in en

as r approaches infinity, Ee always approaches

0

what is Ee useful for

• printers

• tv’s and computer monitors

• x-rays

• radiation therapy

• particle accelerators

charges moving from higher pot en to lower pot en =

useful en

no matter how much charge is moved, each C of charge will undergo the same

change in elec pot en

= elec potential

elec potential

Electric Potential Energy per unit positive test charge

elec potential cont’d

• measured in J/C or volts (V)

• denoted as V

• V = 0 at infinity since Ee is 0 at infinity (ref pt)

elec pot diff

amount of work req per unit test charge to move a pos charge from oe pt to another pt in the presence of an elec field

if charge moves in dir of field, the elec potential

decreases and is converted to kin en and therm en

if charge moves in the dir against the field, the elec potential

increases as work is done against the force of the field which increases Ee

conservative forces

forces not grossly affected by Ff

difficult to analyze motion of particles using newton’s laws directly bc

Fe and a changes as r changes, so it’s better to use conservation of en and include kin en

for 2 like charges

• as charges move farther apart, EE is converted into EK. −∆𝐸𝐸 = ∆𝐸K

• ∆𝐸𝐸 = -∆𝐸K if they are brought together

for two oppo charges

• as charges move farther apart, EK is converted into EE. ∆𝐸𝐸 = -∆𝐸K

• -∆𝐸𝐸 = ∆𝐸K if they are brought together

for parallel plates, the dist b/w plates is

directly proportional to the elec potential difference

in parallel plates, the electric force is

constant, therefore the acceleration of a particle would be constant

elementary charge

the charge of an electron or proton aka 1.602 × 10^-19

the milikan oil drop experiment

an experiment to det the elementary charge

• set-up involves two electrically charged plates, one pos and one neg

• a source of ionizing radiation

• and an atomizer spraying oil onto the top plate

excess number of electrons means the charge is

neg

deficit number of electrons means the charge is

pos

limitations of milikan’s experiment

• accurately calculated the elementary charge

• but could not adequately describe the motion of charged particles due to the presence of charged particles

findings of milikan’s experiment

• each charge was either the elem charge or a multiple of the elem charge

• each charge was never less than 1.602 × 10^-19

the a of particles calculated using newton’s 2nd law is

instantaneous

where is the reference level

at infinity

potential difference

the difference in electric potential in at two different points in a field

volts measure

change in energy per unit charge as batteries and such do work to move the electrons

at infinity, Ee =

0

parallel plate special equations

see notes

accelerating electrons vs protons

electrons start on the side of the negative plate and is propelled through a hole on the opposite plate, aka the positive plate → accelerating protons is the same concept but starts on the pos plate and propelled thru hole in neg plate

no _____ exists outside plates

electric field stren