Role of Charge

Question 1

What forces hold the nucleus together and what is an outline of how this works?

Answer 1

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

Question 2

What is Coulomb’s law?

Answer 2

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

Question 3

What does a negative sign of electrostatic force mean?

Answer 3

An attractive force

Question 4

What is an electric field?

Answer 4

The force experienced by 1C of charge at that point

E= F/ q
Electric Field= Force / Charge

N/C

Question 5

What happens to the strength of electric fields as distances increase in different mediums?

Answer 5

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

Question 6

What is the expression for relative permittivity? What are names for the related constants?

Answer 6

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

​

Question 7

Why does the dielectric constant exist and how does it change?

Answer 7

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

Question 8

What happens when a charged particle moves through an electric field?
What is an equation for this?

Answer 8

Work is done
𝛿 w = −𝑞𝐸 𝛿z
from F=qE, Z is the distance being moved

Question 9

Why is there a negative sign in the electrical work equation?

Answer 9

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

Question 10

What is potential energy?

Answer 10

Energy held by an object due to its position relative to other objects
Energy stored in the field e.g electric, gravitational

Question 11

What is the work done by a particle moving through an electric field in terms of energy?

Answer 11

w= electric energy B - electric energy A
w= U el B - U el A

Question 12

How has the equation for electrical potential energy been derived?

Answer 12

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

Question 13

What is the relationship between force and electrical energy?

Answer 13

Force= - derivative of energy with respect to distance, r

Question 14

What is the electric potential?

Answer 14

V= E/q
electrical energy per unit of charge

Question 15

What is the relationship between electric field and electric potential?

Answer 15

electric field= - derivative of potential with respect to distance, r

Question 16

How can you calculate a constant electric field from height potential difference?

Answer 16

E= potential difference / change in height
= Z 1 - Z 2 / H2 - H1

Question 17

How is electric potential energy and kinetic energy related?

Answer 17

-Change in potential energy = KE
ΔV=ΔU/q
ΔU=ΔVq

-ΔVq= 1/2 mv2

as potential transferred to kinetic

Question 18

What are the vector forms of Coulomb’s equations?

Answer 18

Where r2 is the magnitude of the vector squared, multiplied by the unit vector

Question 19

How can multiple electrical forces be calculated as one?

Answer 19

Cumulative
Add the vector forces

Question 20

How can the electric field be calculated at different distances from the particles?

Answer 20

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

Question 21

When would you have to use the r3 expression for fields?

Answer 21

If the point of interest is the same distance apart from the charged particles, but not the same displacement

Question 22

How do you calculate the work done for non-parallel movement in an electrical field? What about perpendicular?

Answer 22

𝛿𝑤 = −𝑞𝐸𝛿Z
use the parallel component of the distance moved, z
perpendicular, w=0, cos=0

Question 23

Look over

Answer 23

Question 24

In terms of charges, what is a molecule? What is an idealised dipole?

Answer 24

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

Question 25

How can you calculate the potential energy in a constant field?

Answer 25

electrical energy= -qE.r where E and r are both vectors

Question 26

How has the equation for dipole moments been derived?

Answer 26

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

Question 27

How can the dipole moment expression be used?

Answer 27

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

Question 28

How can the dipole moment of a diatomic molecule be calculated?

Answer 28

Set one atom as the origin
μ=∑qr
μ= q1x0 + q2 x r
where r is the bond length

Question 29

How has the dipole moment for a non-linear molecule like water been calculated?

Answer 29

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

Question 30

How has the field of a dipole been calculated?

Answer 30

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

Question 31

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?

Answer 31

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

Question 32

What is the interaction energy between a dipole point in the x axis and the other the z axis?

Answer 32

0
as Uel= μ . E
and the dot product is 0

Question 33

What happens to a dipole as it experiences as electrical force?

Answer 33

By resolving the force into its components
cos= stretching
sin= twisting

Question 34

What is the proof that the origin is independent on dipole moments?

Answer 34