6.2 electric fields

electric field

a region of space where a charged particle is subject to an electrostatic force, a charged object creates an electric field around itself

field

a region of space where a physical quantity which can cause a force (gravitational, electric, magnetic etc) is present at every point

direction of electrostatic force

electrostatic force goes away from a positive charge, and towards a negative charge

repulsion and attraction

like forces repel, opposite forces attract

point charges

protons, electrons and other charged spheres can be modelled as point charges (charge exists at one singular point of infinitely small size)
they have radial lines in the direction of the electrostatic force which show the force getting weaker further from the charge

electric field lines

lines showing the direction and magnitude of an electric force, closer lines mean stronger force and parallel lines mean uniform force

electric field line examples

(inc diagram)

electric field strength

E = F/Q
where E is in NC^-1 and is a vector, F is the electroststic force, and Q is the charge

electric field strength in a uniform field

can also be given by E = V/d
where E is in Vm^-1 and is a vector, V is the potential difference between the plates, and d is the separation between the plates

coulomb's law

the electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation (inverse square law)

coulomb's law equation

for two charges Q and q at distance r:
F ∝ Qq and F ∝ 1/r^2
therefore:
F = kQq/r^2 or F = Qq/4𝜋r^2𝜀0
(inc diagram)

k in coulomb's law

8.99 x 10^9 NM^2C^-3
equal to 1/4𝜋𝜀0
where 𝜀0 is the permittivity of free space

permittivity

the ability of a material to become polarised and store charge
the permittivity of a certain substance can be found by multiplying its relative permittivity 𝜀r by the permittivity of free space

permittivity of free space

8.85 x 10^-12 Fm^-1

electric field strength of a point charge

E = Q/4𝜋r^2𝜀0
where E is a vector, Q is its charge and r is the distance from the charge that the strength is being measured from, and 𝜀0 is the permittivity of free space

REMOVE THIS I THINK ITS NOT IN THE SPEC

a formula for the electric field of a point charge can be created by theoretically bringing a small test charge with negligible charge q, to a larger point of charge Q
the electric field strength on the test charge is expressed by E = F/Q
therefore, using Coulomb's Law, expressed by F = Qq/4𝜋r^2𝜀0
we can get:
E = Q/4𝜋r^2𝜀0

electric field strength and directionality

negative electric field strength means a charge attracts positive charges and positive means it repels them
negative EFS between two charges mean they attract eachother and positive means they repel

gravitational vs electric fields- property that creates the field

gravitational: mass
electrical: charge

gravitational vs electric fields- type of field

gravitational: always attractive
electrical: attract opposite charges, repel like charges

gravitational vs electric fields- field strength

gravitational: force per unit mass g = F/m
electrical: force per unit positive charge E = F/q

gravitational vs electric fields- forces between particles

gravitational: F ∝ Mm, F ∝ 1/r^2
electrical: F ∝ Qq, F ∝ 1/r^2

gravitational vs electric fields- force and field strength

gravitational: F = -GMm/r^2, g = -GM/r^2
electrical: F = Qq/4𝜋r^2𝜀0, E = Q/4𝜋r^2𝜀0
diagram to show similarities
(INC DIAGRAM)

gravitational vs electric fields- shape of field around a point

gravitational: point mass produces radial field
electrical: point charge produces radial field

uniform electric fields

an electric field which has no variation based on position, i.e. two parallel oppositely charged plates
the field lines are completely evenly spaced, and the force exerted is the same anywhere in the field

work done and potential difference

the work done per unit charge when moving a charge from one point to another in an electric field is equal to the potential difference between the two points
V = W/Q

charged particles in a uniform electric field

the movement of charged particles in a uniform electric field can be modelled similarly to that of a massive particle in a gravitational field
(i.e. projectile motion)

electric potential and moving charges

in order to move a charge closer to a like charge, work must be done to overcome the forces of repulsion between them, and in order to move opposite

electric potential at a point

the electric potential at a point is equal to the work done per unit charge to bring a positive charge to that point from an infinite distance away (where it experiences no force)

electric potential equation

the electric potential in a field due to a point charge is defined as
V = Q/(4𝜋𝜀0r)
where V is the electric potential, Q is the charge of the point charge, 𝜀0 is the permittivity of free space and r is the distance from the point charge
(INC DIAGRAM)

capacitance of a point charge

as C = Q/V meaning V = Q/C
and V = Q/(4𝜋𝜀0r)
Q/C = Q/(4𝜋𝜀0r)
thus C = 4𝜋𝜀0r

electric potential and potential difference

the potential difference between two points is equal to the difference between their electric potentials

force-distance graph for a point charge

an F against R graph for a point charge follows an inverse square law shape due to the equation for F having r^2 on the bottom of the fraction
the area of the graph is equal to the work done