Role of Charge Flashcards
What forces hold the nucleus together and what is an outline of how this works?
Strong nuclear force in the nucleus, short range
Responsible for holding quarks together to form nucleons
Leakage of the force outside the nucleons leads to the nuclear force, to form the nuclei
Nuclear force repulsive less than 0.7fm, attractive between 0.8 and 2.5fm, then negligible
In balance with electrostatic repulsion between protons, so nuclei need a certain number of neutrons to be stable
What is Coulomb’s law?
Where q1/q2 are the absolute charges, so may need scaling with the fundamental charge e
E0= is the electric constant for a vacuum, multiply by constant in a different medium
And r is the distance between the particles
What does a negative sign of electrostatic force mean?
An attractive force
What is an electric field?
The force experienced by 1C of charge at that point
E= F/ q
Electric Field= Force / Charge
N/C
What happens to the strength of electric fields as distances increase in different mediums?
Electric fields fall off more rapidly through matter than a vacuum
This is because the dielectric constant
εr increases in matter, so a smaller force
What is the expression for relative permittivity? What are names for the related constants?
ε= εr x ε0, this is permittivity
ε0= vacuum permittivity, electric constant, C2N-1m-2
εr= relative permittivity, dielectric constant , no units
εr is used as a scale factor to increase ε0 depending on the medium
Why does the dielectric constant exist and how does it change?
A bulk property, relying on a uniform polarisable material between charges
As dipoles in the solvent line up in the field, they reduce the field
Atom=1, but when several molecules between charges (i.e solvent in between charged particles) , change to εr
As charges approach more closely to each other approach ε0
What happens when a charged particle moves through an electric field?
What is an equation for this?
Work is done
𝛿 w = −𝑞𝐸 𝛿z
from F=qE, Z is the distance being moved
Why is there a negative sign in the electrical work equation?
If the force is in the same direction as movement, w<0 as using F from the field for work
If in an opposite direction, equation gives a positive value, as energy transferred to overcome force
What is potential energy?
Energy held by an object due to its position relative to other objects
Energy stored in the field e.g electric, gravitational
What is the work done by a particle moving through an electric field in terms of energy?
w= electric energy B - electric energy A
w= U el B - U el A
How has the equation for electrical potential energy been derived?
dw= -F dr
integrating the equation
w= q1q2/4𝜀π (1/Rb - 1/Ra) + C
w= change in electrical energy
so electrical energy= q1q2/4𝜀π r
and C=0 at infinite separation
What is the relationship between force and electrical energy?
Force= - derivative of energy with respect to distance, r
What is the electric potential?
V= E/q
electrical energy per unit of charge
What is the relationship between electric field and electric potential?
electric field= - derivative of potential with respect to distance, r
How can you calculate a constant electric field from height potential difference?
E= potential difference / change in height
= Z 1 - Z 2 / H2 - H1
How is electric potential energy and kinetic energy related?
-Change in potential energy = KE
ΔV=ΔU/q
ΔU=ΔVq
-ΔVq= 1/2 mv2
as potential transferred to kinetic
What are the vector forms of Coulomb’s equations?
Where r2 is the magnitude of the vector squared, multiplied by the unit vector
How can multiple electrical forces be calculated as one?
Cumulative
Add the vector forces
How can the electric field be calculated at different distances from the particles?
force= q1q2/ 4piε0r2
field= force per unit charge, divide by q
field= q / 4piε0r2
and replace r with magnitude of r which you square x unit vector
Use the distances from each charged particle to the point of interest to calculate the fields
Then add them, factorise if need be
See slide for example
When would you have to use the r3 expression for fields?
If the point of interest is the same distance apart from the charged particles, but not the same displacement
How do you calculate the work done for non-parallel movement in an electrical field? What about perpendicular?
𝛿𝑤 = −𝑞𝐸𝛿Z
use the parallel component of the distance moved, z
perpendicular, w=0, cos=0
Look over
In terms of charges, what is a molecule? What is an idealised dipole?
A molecule is an ordered array of charges, with electrical properties characterised as a series of effects of diminishing magnitude and range
Dipole: separation between equal and opposite charges, field lines from pos to neg
How can you calculate the potential energy in a constant field?
electrical energy= -qE.r where E and r are both vectors
How has the equation for dipole moments been derived?
Uel= ∑ qEr where E and r are vectors
as in a constant electric field,
μ=∑qr
and so Uel= μ x E
in C m or Debye
How can the dipole moment expression be used?
μ=∑qr
here q is the partial charges, which will be equal and opposite
And r is the distance from the origin which you can decide
where the vectors move from negative to positive
How can the dipole moment of a diatomic molecule be calculated?
Set one atom as the origin
μ=∑qr
μ= q1x0 + q2 x r
where r is the bond length
How has the dipole moment for a non-linear molecule like water been calculated?
Set the central atom as the origin and calculate the remaining electrical energies with μ=∑qr
Separate the vector in x,y components, and then one set will cancel
How has the field of a dipole been calculated?
Taking a test point, and calculating the electric field at that point by summing the electric fields from each of the ends of the dipole
Ends up simplifying to 2μ/4piε0r3
- as takes into account the vector with the dipole moment
- assumes r is much larger than the distance between the ends of the dipoles
How can you calculate the interaction energy between two dipoles, 1 at the origin, and 1 at a distance away on the z axis, pointing at towards the z axis aswell?
2nd molecule electric field experienced dependent on the dipole of the first
E at 2= 2μ/4piε0r3
Uel= -μ . E dot product
where μ is the dipole moment of this second molecule
What is the interaction energy between a dipole point in the x axis and the other the z axis?
0
as Uel= μ . E
and the dot product is 0
What happens to a dipole as it experiences as electrical force?
By resolving the force into its components
cos= stretching
sin= twisting
What is the proof that the origin is independent on dipole moments?
