electric fields Flashcards
what does any object with charge have, and what does this charge allow them to do?
EF
any object with charge has an electric field around it - a region where it can attract or repel other charges
what is electric charge (Q) measured in?
EF
electric charge (Q) is measured in Coulombs (C)
can electric charges be positive or negative?
EF
yes
what do oppositely charged particles do to each other?
EF
oppositely charge particles attract each other
what do like charged particles do to each other?
EF
like charges repel each other
what does a charged object experience if placed in an electric field?
EF
if a charged object is placed in an electric field, the charged object will experience a force
how does a charged object act, if it is a sphere with evenly distributed charge? and what does this mean?
EF
⋅ if a charged object is a sphere, with evenly distributed charge (spherically symmetrical), it will act as if all of its charge is at its centre
⋅ so you can model it as a point charge (at distances larger than its radius)
how large does a distance have to be, to model a charged object as a point charge?
EF
you can model a charged object as a point charge, as long as the distances are larger than the charged object’s radius
how are electric fields represented on a field diagram?
EF
just like with gravitational fields, electric fields can be represented by field lines
what do you use coulomb’s law to work out?
EF
you need coulomb’s law to work out F electric
what is F electric?
EF
F electric is the force of attraction or repulsion between two point charges (or two objects that behave as point charges)
what does it mean if F electric is negative?
EF
⋅ if F electric is negative, this means that the force is attractive
⋅ this is bc the charges (Q and q) must be opposite for F electric to be negative
[⋅ bc F = kQq/(r^2)
⋅ when there are opposite charges (eg, a proton and an electron) that attract each other, one will be positive (the proton or positively charged ion) and one will be negative (the electron or negatively charged ion)
⋅ so when you multiply Q by q, you will be multiplying a positive with a negative
⋅ so you will end up with a negative force]
what does it mean if F electric is positive?
EF
⋅ if F electric is positive, the force between the charges is repulsive
⋅ this is bc charges (Q and q) must be like for F electric to be positive
[⋅ bc F = kQq/(r^2)
⋅ when there are like charges (eg, a proton and a proton) that repel each other, one will be one charge (eg, a proton or positively charged ion) and the other will be the same charge (another proton or positively charged ion)
⋅ so when you multiply Q by q, you will be multiplying a positive with another positive (or a negative with another negative)
⋅ so you will always end up with a positive force]
what is coulomb’s law?
EF
coulomb’s law is:
what is the relationship between the forces on Q and q?
EF
the force on q is always equal and opposite to the force on Q
what kind of law is coulomb’s law an example of, and why?
EF
⋅ coulomb’s law is an example of the inverse square law
⋅ bc the further apart the charges are, the weaker the force between the charges
what does k stand for in coulomb’s law?
EF
⋅ k is the electric force constant (or Coulomb’s law’s constant of proportionality)
⋅ k is equal to about 9.0 x10^9 N m^2 C^-2
⋅ you’ll be given k’s value in the exam, either in the data and the formula booklet, or in the question
what is electric field strength?
EF
electric field strength is defined as the force exerted[/acting] per unit positive charge
what is another way of describing electric field strength?
EF
electric field strength is the force that a charge of +1 C would experience if it was placed in an electric field
what is the equation to work out the electric field strength (E electric) (using F and q)?
EF
what does E electric also represent?
EF
E electric is also a vector pointing in the direction that a positive charge would move
what are the units for electric field strength?
EF
the units for electric field strength are N C^-1
what does the electric field strength depend on?
EF
the electric field strength often depends on where you are in the electric field
what type of field does a point charge have?
EF
a point charge (or any body that behaves as if all of its charge is concentrated at its centre) has a radial field
what relationship does E electric have with r in a radial field?
EF
in a radial field, E electric is inversely proportional to r^2
what does E electric depend on in a radial field?
EF
in a radial field, E electric depends on the distance r from the point charge Q (or from the centre of the source of the radial field)
what is the equation for electric field strength in a radial field (E electric)?
EF
what direction do field lines point for a positive charge?
EF
what direction do field lines point for a negative charge?
EF
what direction do electric field lines point?
EF
⋅ electric field lines point in the direction that a positive charge would move in an electric field
⋅ (so a positive charge would move away from a positive charge [which is why field lines point away from positive point charge] and positive charge would move towards a negative charge [which is why field lines point towards a negative charge])
⋅ electric field lines also go from positive to negative
what should field lines for a point charge look like?
EF
what law does E electric also follow?
⋅ E electric also follows the inverse square law
⋅ bc E electric ∝ 1/(r^2)
what does the graph of electric field strength (E) against r look like, and what does this show?
cgp uses E electric instead of E fsr
⋅ the graph shows that the electric field strength decreases as you go further away from Q (if you looked on an electric field line diagram, the field lines get further apart as r increases)
does a charge in an electric field have electric potential energy?
EF
yes
what is electric potential energy?
EF
electric potential energy is the work done in moving a [small] positive charge from infinity to a point in an electric field [/ a distance r away from the point charge Q]
what is the equation for electric potential energy?
EF
what does the electric potential energy against r graph look like for a repulsive field?
EF
(graph is positive bc in repulsive field GPE is positive)
what does the electric potential energy against r graph look like for an attractive field?
EF
(graph is negative bc in attractive field GPE is negative)
what do these electric potential energy against r graphs show?
at an infinite distance from Q, the charged particle q would have zero electrical potential energy
in an ATTRACTIVE field, what happens to the electrical potential energy of charge q as r INCREASES?
EF
• in an ATTRACTIVE field (eg, Q negative and q positive), charge q gains electrical potential energy as r INCREASES
• bc have to do work against attractive force on charge q to move it AWAY from point charge Q, so energy is transferred to charge q
in a REPULSIVE field, what happens to the electric potential energy of charge q as r DECREASES?
EF
⋅ in a REPULSIVE field (eg, Q and q are both positive), you have to do work against the repulsion to bring q closer to Q
⋅ so the charge q gains electric potential energy as r DECREASES
what is the area under an electrical force (F electric) between r1 + r2 against r graph?
EF
⋅ for a point charge q (and therefore also for any spherical charge) you can plot the electric force (F electric) against distance (r) from a charge producing the electric field
⋅ this graph is an example of the inverse square law
⋅ the area under an F electric against r graph between r1 + r2 (bc area under whole graph would be undefined bc graph doesn’t touch x-axis) is the change in electric potential energy
how do you move a unit charge between two distances (r1 + r2) and change the unit charge’s electric potential energy (EPE)?
EF
⋅ to move a unit charge between two distances (r1 + r2) and change its EPE, you have to apply force and do work on the charge
⋅ this force applied is equal to the electric force
what is the electric potential (V electric)?
EF
the electric potential (V electric) is the work done in moving a unit positive charge from infinity to a point in an electric field
as electric potential is the work done in moving a unit positive charge from infinity to a point in an electric field, what does that mean?
EF
this means that at infinity, the electric potential will be zero
what does electric potential equal (for a small charge [q] at a distance r away from the point charge [Q])?
EF
⋅ V electric = electric potential energy/q
what does V electric also equal?
EF
when is V electric positive and when is V electric negative?
EF
as with electric potential energy, V electric is positive when the force is repulsive, and negative when it is attractive
what do equipotentials show?
EF
equipotentials show all the points in a electric field which have the same electric potential
what happens when a charge travels along the line of an equipotential?
EF
if a charge travels along the line of an equipotential the charge doesn’t lose or gain energy (no work is done)
what is the equation for E electric in a uniform field?
EF
E electric = V/d
where:
* V = pd between plates
* d = distance between plates
what shape are the equipotentials for a point charge (or spherically symmetric charge)?
EF
⋅ for a point charge (or spherically symmetric charge), equipotentials are spherical surfaces
(⋅ the circles are the equipotentials, the straight lines pointing towards Q are field lines
⋅ the diagram shows equipotentials of -60, -50, and -40 V around the point charge Q)
what directions do equipotentials point relative to field lines?
EF
equipotentials and field lines are perpendicular to each other
how is electric potential linked to the electric field strength?
EF
the electric field strength (E electric) is equal to the negative of the rate of change of the electric potential with respect to the distance
in what directions do the electric force and the electric potential move relative to each other in order to increase EP or electric PE?
EF
• the electric force and the electric potential/electric PE of a charge act in opposite directions in order to increase the electric potential/electric PE of the charge (according to the tip)
• as you have to do work against force
what does it mean if E electric is equal to the negative rate of change of V electric with respect to distance?
EF
⋅ this means that E electric can also be measured in V m^-1
⋅ and the gradient of the graph of V electric against r is E electric, as seen in the graph (repulsive field used just as eg)
what does the area under the graph of E against r (between two distances) give?
EF
the area under the graph of E electric against r (between r1 and r2) gives the change in V electric
does the electric field strength change in a uniform field?
EF
no, the electric field strength is the same everywhere in a uniform field
how can a uniform field be produced, and what do the field lines and equipotentials look like between the plates?
EF
⋅a uniform electrical field can be produced by connecting two parallel plates to the opposite poles of a battery
⋅ the field lines move from + V plate to 0 V plate, they are parallel to each other and are evenly spaced
⋅ the equipotential surfaces are parallel to the plates, and perpendicular to the field lines
⋅ equipotentials are also evenly spaced and symmetric
what are 4 of the similarities between gravitational and electric fields?
EF
where does the equation for electric field strength for a uniform field (E electric = V/d) come from?
EF
⋅ the formula (E electric = V/d) comes from the equation for E electric = - d(V electric)/d(r)
⋅ bc the rate of change of potential is constant for a uniform electric field
what are the differences between gravitational and electric fields?
EF
some of the differences between gravitational and electric fields are:
1) gravitational forces are always attractive, whereas electric forces can be either attractive or repulsive
2) objects can be shielded from electric fields, but not from gravitational fields
3) the size of the electric force depends on the medium between charges (eg, plastic or air), whereas for gravitational forces, this makes no difference
⋅ (bc electric force takes into account permittivity of free space (or material between charges) with k whereas gravitational force doesn’t
what do you replace ε0 with if you’re not working in free space?
EF
you replace ε0 (permittivity of free space) with ε1 (permittivity of the substance)
what law does millikan’s oil-drop experiment make use of?
EF
millikan’s experiment used stoke’s law
when does an object experience a viscous drag force and what is this viscous drag force due to?
EF
⋅ when you drop an object into a fluid (like air) it experiences a viscous drag force
⋅ the viscous drag force is due to the viscosity of the fluid
what direction does the viscous drag force act in?
EF
the viscous drag force acts in the opposite direction to the velocity of the object
how does the drag force change with an object’s velocity[/speed]?
EF
the drag force increases with an object’s velocity[/speed]
how do you calculate the viscous drag force on a spherical object using stoke’s law?
EF
what is the basic set up for millikan’s experiment?
EF
the set-up for millikan’s experiment was:
1) atomiser created fine mist of oil droplets that were charged by friction (against walls of atomiser) as they left atomiser (positively if they lost electrons, negatively if they gained electrons)
2) some of droplets fell through hole in top plate + could be viewed through microscope. (eyepiece carried scale to measure distances - and so velocities - accurately)
how did millikan find the radius of the charge before his experiment?
EF
before millikan’s experiment (before the electric field was switched on), millikan found r by:
1) before the electric field is switched on, the only forces acting on each oil droplet are:
a) the weight of the drop (equal to mg) acting downwards on the oil droplet
b) the viscous drag force from the air acting upwards on the oil droplet
2) the drop will then reach terminal velocity (i.e. it will stop accelerating) when these two forces become equal (mg = 6πηrv)
3) by equating the weight (using mass in terms of volume + density) to stokes law (and finding ρ + η in separate experiments), millikan found r
[4/3πr^3ρg = 6πηrv, which then => r^2 = 9ηv/2ρg]
4) this r could then be used when millikan switched on the electric field in millikan’s experiment
what did millikan find in his experiment?
EF
⋅ millikan repeated millikan’s experiment for hundreds of droplets and found that the charge on any drop was always a whole number multiple of 1.60 x10^-19
⋅ these results suggested that charge was quantised
⋅ millikan also concluded that charge can never exist in smaller quantities than 1.60 x10^-19 and assumed that this was the size of the charge carried by the electron
what should you consider when using electronvolts?
EF
⋅ do NOT confuse the unit electron volt (eV) with the equation for electric potential energy (= qV), they are separate things
⋅ electric potential energy can also be written as E = eV which is why it can be confusing
can charged particles be deflected by magnetic fields?
EF
yes
why are charged particles deflected by magnetic fields?
EF
⋅ charged particles can be deflected by magnetic fields because a magnetic field exerts a force on particles
⋅ this is the same effect as where a magnetic field exerts a force on a current-carrying wire
why do current-carrying wires experience a force in a magnetic field?
EF
⋅ electric current in a wire is caused by the flow of negatively charged electrons
⋅ forces act on charged particles in a magnetic field
⋅ so these charged particles are affected by magnetic fields - so a current-carrying wire experiences a force in a magnetic field
how do you obtain the equation F = Bvq (magnetic force/electromagnetic force on wire)?
EF
1) the equation for the force exerted on a current-carrying wire in a magnetic field is: F = BIL
(l is a lowercase L but bc it looks like an uppercase i im going to replace l with L in equations)
2) to see how this relates to charged particles moving through a wire, you need to know that electric current (I) is the flow of charge (q) per unit time (t): I = q/t
3) as shown in the diagram, a charged particle that moves a distance l in time t has the velocity v: v = L/t => t = L/v
4) substituting this equation for time (t = L/v) into the previous equation for current (I = q/t) gives the current in terms of the velocity of the charge flowing through the wire: I = qv/L
5) putting I = qv/L back into F = BIL gives electromagnetic force on wire as F = qvB
(where B = magnetic flux density, v = particle velocity, q is charge on particle)
what can you find using the equation F = Bqv [or F = qvB]?
EF
you can use F = Bqv to find the force acting on a single charged particle moving through, and perpendicular to, a magnetic field
what is the equation for the electromagnetic force acting on a single charged particle moving through + perpendicular to a magnetic field?
EF
F = Bqv
in what way are charged particles deflected in a magnetic field?
EF
charged particles in a magnetic field are deflected in a circular path
what direction does the force acting on a moving charge in a magnetic field act in, and what motion does this satisfy the condition of?
EF
⋅ by applying fleming’s left-hand rule, we know that the force on a moving charge in a magnetic field is always perpendicular to the charge’s direction of travel (aka the current)
⋅ mathematically, the fact that force always acts perpendicular to the charge’s direction of travel (so towards the centre of a circle) is the condition for circular motion
how is the deflection of charged particles in a circular path in a magnetic field used in the real world?
EF
⋅ particle accelerators (such as cyclotrons + synchrotrons) use this effect
⋅ particle accelerators use high electric and magnetic fields to accelerate particles to very high energies along circular paths
why is knowing the radius of the curvature of the path of a charged particle moving through a magnetic field useful?
EF
⋅ the radius of the curvature of the path of a charged particle moving through a magnetic field gives you information about the particle’s charge and mass
⋅ this means you can identify different particles by studying how they’re deflected
what doe the centripetal force acting on a charged particle tell us?
EF
the centripetal force tells us about the particle’s path
what are the centripetal force and the electromagnetic force equivalent for?
EF
the centripetal force and electromagnetic force are equivalent for a charged particle travelling along a circular path
how can you find the equation for the radius of a charged particle’s circular path when deflected by a magnetic field?
1) for a uniform motion newton’s 2nd law of motion gives:
F = m(v^2)/r
2) so, for a charged particle following a circular path in a magnetic field (where F = Bqv):
Bvq = m(v^2)/r
3) rearranging gives:
r = mv/Bq
what does r =mv/Bq tell us about different charged particles?
EF
⋅ different charged particles will have paths with different radii
⋅ the higher the ratio of m to q, the larger the radius of the circular path
how did millikan find the charge of a charged particle in millikan’s experiment?
EF
during millikan’s experiment (after switching on electric field):
1) when millikan applied a pd between the plates, an electric force is exerted upwards (from negatively-charged bottom plate) on the (negatively-charged) oil dropets, repelling the oil droplets
2) millikan adjusted applied pd, to alter the electric field strength, until each oil droplet was stationary
⋅ since viscous force[/drag] is proportional to velocity of object, once each drop stopped moving, viscous force disappeared
3) once the viscous drag force disappeared, only two forces were acting on the oil droplet:
a) the weight of the droplet acting downwards on the droplet
b) the electric force due to the uniform electric field acting upwards on the oil droplet
4) since the oil droplet is stationary, this electric force must equal weight, so: qV/d = 4/3πr^3ρg
5) using the r calculated initially, millikan calculated q of the oil droplet using this equation (qV/d = 4/3πr^3ρg)
what are the units for electric field strength (E)?
EF
N C^-1
or
V m^-1
what are the units for electric potential (V)?
EF
J C^-1
or
V
what is the unit for electrical force (F)?
EF
N
what is the unit for the electric potential energy?
EF
J
is electric field strength (E) a vector or scalar?
EF
electric field strength (E) is a vector (bc it’s linked to electric force + force is a vector)
is electrical force (F) a vector or scalar?
EF
electric force (F) is a vector
is electric potential (V) a vector or scalar?
EF
electric potential is a scalar (bc it stems from electric potential energy + energy is scalar quantity)
is electric potential energy a vector or scalar?
EF
electric potential energy is a scalar
what are all the equations you can use for radial fields?
EF
F = kQq/(r^2)
electric potential energy = kQq/r
E = kQ/(r^2)
V = kQ/r
(here V means electric potential)
what are all the equations you can use for a uniform field?
EF
E = V/d
F = qV/d
(V here means voltage)
what equations can you use for both radial fields and uniform fields?
EF
F = EQ
kinetic energy = qV
or
electric potential energy = qV
F = electric energy/d (basically work done eq rearranged)
what are misc equations for this topic?
EF
F = Bvq
F = m(v^2)/r
r = mv/BQ
what does permittivity mean?
EF
⋅ permittivity is “the extent to which a medium concentrates lines of electrostatic flux [electric field lines]”
⋅ basically permittivity = how well an electric field can be set up in a material
what shapes do the equipotentials make in a radial field?
concentric circles around the point charge w increasing space between them
[INSERT DIAGRAM FROM PP]
“explain why equipotentials w an equal pd between them have consecutively greater spacing the further from the charged particle they are” [3 marks]
⋅ field strength decreases w distance from the particle
⋅ equal potential differences mean the same amount of work is done to move a unit charge from one equipotential to the next
⋅ work done = force x displacement so to do the same work against a weaker field then the charge must move through a greater distance
⋅ hence equipotentials are more distantly spaced further away from the particle
this question is about electric charge
a) a plastic rod XY is held at end X. end Y is rubbed with piece of cloth and, as result, the end Y becomes electrically charged
the procedure is now repeated using a copper rod and it is found that the copper rod remains electrically neutral. explain these observations in terms of the properties of conductors + insulators
⋅ in plastic there are no free electrons
⋅ but electrons can be transferred from cloth
⋅ leaving imbalance of charge on rod
⋅ electrons can move more freely in copper
⋅ electrons are transferred to cloth from rod
⋅ bc copper body is conductor
⋅ electrons will flow from earth leaving rod neutral
this questions is about the forces on charged particles in magnetic + electric fields. the diagram below shows part of device for measuring speed of alpha particles. all of the apparatus in a vacuum
alpha particles emerge through hole in shield around the source + pass between pair of flat, parallel electrodes. the bottom electrode is 0 V
[insert diagram]
