Chapter 22 electric Fields Flashcards
What is a field in physics
A region where an object will experience a force at a certain distance due to some property they have
For example mass or vharge
Where do electric fields come from
Any charged particle will have its own electric field, and thus if another charged particle was placed in this field a force would be entered on it
What is the electric field show (the firce or direction what charge will face)
Electric field shows the direction of force experience by a POSITIVE CHARGE
Negative field lines thus pointing in to them and will go reverse
What is the equation for electric field strength
E=F/Q
The force felt per unit charge at that point shows you the electric field strength at that point
Electric fuel strength is a vector quantity so what direction
Same direction as firce
, it’s the direftuojn a positive charge would move when placed at the point
R,ember what are basic facts about electric field lines
Closer they are stringer field, if parallel then uniform field
How can we model the electric field on uniform spheres or point charges?
As RADIAL fields, thus we can use equations to show how the electric field strength decreases with increase of radius
What does coloumbs law describe
The firce experienced by BOTH charged particles due to electric fields
Experienced by both due to newtons 3rd law , force exerted on each other will be equal in MAGENTIC use but opposite in direction
What is Coulomb’s law
F = Qq/r2 (4pi episilom 0)
Essentially the firce experience by two POINT CHARGES (has ti be radial fields, can model Sphered as point charges too) is proportional to the product of their charges and INVERSELY proportional to the square of their separation from the centre .
Thus we have a proportional constant, and this is 1/ 4PI x permitivity of a vacuum
Why can we model spheres uniform as POINT CHARGES? (And all of newtons laws were point )
Looking at it from afar looks like a point charge that’s why
So what’s Columbia equation in full
F = Qq/ 4piE0r2
How else can we now write down equation for electric field
E=f/q
The electric field strength at a distance r is equal to the firce field by a POSITIVE TEST CHARGE , divided by the charge of it , thus qcancel
(Sub in f =Qq formula)
So E= Q/ 4piE0r2
Simlaotiy to grav fields?
g = F/M
F= GMm/r2
So g = GM/r2
Same kinda thing
Both are assuming you have POINT MASSES of radial FIELD LINES
Key difference between grav field and elec field
Is that grav field is always attractive but elec can be repulsive too
For a system of two parallel plates where one is charged positive and other negative with a potential difference, what is the electric field strength between them shape?
Parallel lines = thus uniform field between them
What’s the electric field strength between two PARALLEL. Plates OR ANY UNIFORM FIELD charged by a potential difference
How to derive
E=V/d
All you need is voltmeter and measure the separation
This formula comes from v = wd/q, and wd = fxd, and sub in equation for f from e=F/Q
What even is a capacitor
A capacitor is an electric,a component that essentially stores charge when a pod is applied across it, and then can discharge this when attached ti something else
How does a capacitor store charge or in ither words what happens when the circuit first starts
Electrons go from one terminal to one plate and build up as that’s all they can do . At this point it repels electrons from surface if other player making it positive . As electrons can’t go anywhere they stay here until discharged.
This is possible by connecting wire to some other component and electrons will flow back as they want to be stable
This happens in a flashlight from a phone
What is capacitance then
A measure of how much charge can be stored on a parallel plate based on how much voltage is applied
C= Q/V
This is a constant on the Q against v graph as gradient
And depends on conditions of plate and insulator in between
What is the unit for cappacistsnce
This is Farrad , but CV-1
And seen as tho C is the gradient of Q against v graph what’s the energy stored by a cappacsit
And what is this energy is a fraction of total energy in ANY CIRCUIT , and why is that?
Well v = energy/Q, so energy = V x Q, which is precisely the area under our graph
So energy = 1/2VQ
2) if total energy is vQ it means capacitor always takes half energy, and other half is always loss in resistance and wires
How else write energy equation for cappacitorn
If E = 1/2VQ, and C= Q/V, then Q= CV
And E= 1/2cV2
So with a cappator again where is half the energy always gone
Lost to heat always and half energy taken by cappator
Back to electric field topic and cappaticne , we now know capacitance is a measure of how much charge can be stored on a parallel plate compared to voltage supplied,
what other factors would increase the amount of charge with one volt? (3)
1) The greater the area of the plate means MORE CHARGE can be held
2) the less the distance means more charge can be held too as further away harder ti hold
These are thus proportional, but we must also consider the “material “ we are in, as for different materials we will have different values
Thus this gives us a proportionality constant of the permitivity of the material capacitance is happening through, called a DIELECTRIC
Thus what is the EQUATION for capacitance in this case
C = E x Area/ distance
What even is permitivity “
Permitivity Is a measure of how string sn electric field can be made in this material
How can we work out the permitivity if other dielectrics
Given the relative permitivity of them in compared to the permitivity if a vacuum , we know e = er x e0
Where er is relative
And e0 is vacuum
So two equations for capacitance now in a parallel plate
C = Q/V
C = e x Area / distance
So how can you do an experiment quick to determine permitivity if material
Using capacitor and coloummeter etc (pretty good) (equate equations)
With different voltages charge up a capacitor
Then discharge the capacitor by disconnecting and attaching wire to coloumb meter = this will tell you the charge collected by capacitor based on the voltage supplied
Collect different results based on different voltages
2) now equate cappatiacne equations and plot a graph of Q against V , identifying the gradient
Using separation and area, rearrange the value of gradient for E!
What about projectile motion with charged particle in an electric field between two parallel plated. How can we work out and why
As parallel = uniform electric field
As uniform = CONSTANT force exerted on particle wherever it is
Constant force = constant acceleration
Knowing the acceleration, you can work out final speed knowing horizontally nothing changes as no acceleration in that direction
Need equation for a, A = F/M , and F = EQ, and E = V/D, make equation find A and use SUVAT
Finally use trig for final velociytn
Now what is difference and definition of electric potential energy and electric potential
Electric potential energy is the total work done needed to bring a particle of positive charge from infinity to a separation r in sn electric field of another positive charged particle without acceleration
Electric potential is the total work done per UNIT CHARGE in brining a particle from infinity to that point without acceleration Etc
How to get equations for epe and potential
Epe two ways to think about it
1) graph of Force against distance is inverse square law, and extends till Infinity (asymptomatic)
- as work done is always area under graph, to get total energy needed form I fnity to r , need to integrate area from infinity to r
2) yh basiclaly what’s happening nis thr force is changing closer you get, but over a small distance dr it’s assumed constant. So work done over this small distance is dr x f, and integral of this from infinity to r gives you total work done
How to get equation for potential
Potential is defined is work done form unfit etc per unit CHARGE.
If test charge is q, then jus put equation for epe in and cancel q
So what is equation for potential energy
EPE= Qq/ 4PI E0 r
And what is equation for potential
Potential = Q/ 4Pi E0r
What happens if one of the charges are negative , what does this mean for value of epe
Yh epe will also be negative but this jus means it’s attractive force so energy need to pull them away
Units for electric potential
Volts
So what is potential different electric
Simply the different in potential between two points , this what voltmeter does
When doing and deriving equaruon for potential what is assumed potential at infinity
By dfeifntjin the work done from infinity to infinity would be 0 so potential 0 too
Okay so what is a capacitor again
If a sphere has charge isolated is it a capacitor?
Capacitor is an object thst stored charge
Yes because it stored charge
Thus this must have capacitance based on distance
Derive equation of capacitance for a sphere of charge q
As c = Q/V
And we know now Q= 4pie0rV
Then V cancel out
So capacitance for a sphere = 4piE0r
How can earth be modelled as a capacitor or in space
Just needs radius and it has capacitance that’s why
So in a sphere what’s the only thing that determines capacitance interestingly
Just the radius !
Finally what is equipotentisl lines
These are lines in which the potential is the same so there can be no potential difference between them and energy difference either (I think)
Okay so in that question uniform electric field so infirm firce, why is work done only downwards
As work done is force time displacment cos theta or displacment in direction of force, sideways there is no force (bun equipotential), but there is a constant force down in the direction
So wd = fd
And f = eq
But in questions where it isn’t a constant force but rather radial, need to integrate instead
This why wd = KQq/ r
How to find the net potential due to certain charges at a point?
Find the Indian potentials cashed by charged and add them up
How to find net electric field by different charged
Here draw the radial field lines and here you gonna have to cancel out using components !
Identify the ones which cancel or sum
Can a point have zero potential and net electric field, give Verna or none at all
Yes! Remember potential is infinity to that point so irrespective of the field
Field depends on surrounding fields
Finally what to do in net electric field problem
Once found horizontal and vertical = pythag
In general find net electric field how
Jus isolate the charged and use formula if electric field due to point charge
10 new formulas name them
Electric field definition
Force due to two charges electric field
Electric field due to point charge
Electric field in parallel plate with voltage capacitor
Equation for capacitance
Equation for cappacitsnce with variables in parallel plate
Equation for permitivity
Definition of epe (potential ) and equation
Potential equations
Cappaciatsnc in a sphere
Work done in a parsley plate on electron
= vQ
