Y2: Gravitational and Electric fields Flashcards
What is a force field
A region in which an object experiences a non-contact force
What is a radial field
A field surrounding a central point in which the force decreases as the distance increases (Field lies move further apart).
What is a uniform field
A field in which all filed lines are parallel, and equally spaced, so the force is constant at all points within the field
When can gravity be considered as a uniform field
Close to the surface, as the field lines are (almost) parallel
What is Newton’s Law of gravitation
F = -GMm/(r^2)
(Negative as always acts towards the centre of the larger mass)
F: Magnitude of the force
G: Gravitational constant (6.67x10^-11)
M & m: Masses of the 2 objects
r: Distance between the centre of the two masses
What is the gravitational constant (G)
6.67x10^-11 (Nm^2kg^-2)
Why can Newton’s Law of gravitation be described as an inverse square Law
F ∝ 1/(r^2)
∴ The force becomes weaker at a greater distance
This is because Gravitational fields are radial:
- If a sphere is drawn around the centre of mass, radius r, all points on the sphere will experience the same force
- SA = 4π(r^2)
- ∴ x2 Radius, SA = 4π((2r)^2) = 4(4π(r^2))
- This means the surface area of the sphere increases by the square of the scale of the increase in r (SA ∝ r^2)
- The force ∝ 1/SA (field lines spread out)
- ∴F ∝ 1/(r^2)
What is Gravitational field strength (g)
The force per unit of mass of an object in a gravitational field
What is the equation for gravitational field strength in a uniform field
g = F/m
(Constant in uniform fields)
What is the equation for gravitational field strength in a radial field
g = GM/(r^2) = -ΔV/Δr
∴ Depends on the distance from the object
(Derived by dividing the force from Newton’s Law of gravitation by m)
What is the value for the gravitation field strength of earth (at the surface)
9.81 (Nkg^-1)
What is shown by the area under a graph of gravitational field strength against radius
Gravitational potential
What happens when gravitational fields are combined
Gravitational fields are vector fields, so gravitational field strengths can be added to calculate the combined effect on an object within multiple fields
What is gravitational potential (V)
The energy required to move a unit mass from infinity, to a point within the field.
(Jkg^-1)
(GPE of a unit mass)
Why is gravitational potential negative
Gravitational potential at infinity = 0
∴ Objects closer to the mass have negative potential, as work needs to be done against the field to lift them back to infinity
What is the equation for gravitational potential (in a radial field)
V = -GM/r
Energy to move the unit mass is equal to the work done
Work done = Force x distance
F = g = -GM/(r^2)
(m = 1, for unit mass)
d = r
∴ gr = (-GM/(r^2))r
∴ W = -GM/r
∴ V = -GM/r
What is shown by the gradient of a graph of Gravitational potential against radius
Gradient = -g
(-ΔV/Δr = g)
What is gravitational potential difference
The energy needed to move a unit mass between two points at different distances r from M, in a gravitational field.
(Work done per unit mass)
What is the equation for the gravitational potential difference (in a radial field)
ΔV = -GM/Δr = ΔV2-ΔV1
Potential difference = initial potential - final potential
∴ ΔV = ΔV2-ΔV1
∴ ΔV = -GM/Δr
What is the difference between ‘the change in gravitational potential’, and the ‘gravitational potential difference’
- Change in gravitational potential =
The difference in gravitational potential between two points in a gravitational field, where gravitational potential is 0 at infinity - Gravitational potential difference =
The energy required to move a unit mass between two points in a gravitational field
Both are represented as ΔV, and are pretty much the same thing, but are defined slightly differently
What is the equation for work done in a gravitational field
ΔW = mΔV
(change in GPE)
Work done = Force x distance
F = -GMm/(r^2)
d = Δr
∴ Fd = (-GMm/(r^2))r
∴ ΔW = -GMm/r
ΔV = -GM/Δr
∴ ΔW = mΔV
What is gravitational potential energy
The energy required to move a mass m from infinity, to a point within the field. (Gravitational potential of mass m)
What is the equation for the gravitational potential energy in a radial field
Ep = -GMm/r
Work done = mΔV
Energy required is equal to the work done
∴ Ep = mΔV
ΔV = -GM/Δr
∴ Ep = -GMm/r
What is the equation for Gravitational potential energy in a uniform field (g is constant)
Ep = mgh
(Positive, as the earth’s surface is taken to be 0 close to the surface)
This is derived from the equation for Ep in a radial fields, using h (Δr) instead of r
m = m
g = GM/(r^2)
h = (Δ)r
∴ mgh = m(GM/(r^2))r
∴ GMm/r ⇒ mgh
What are equipotentials
Lines (2D) or surfaces (3D) that join together all the points within a field that have the same gravitational potential
- Are perpendicular to field lines
- Objects traveling along equipotentials have the same V
(Ep = 0)
What are satellites
Any smaller mass that orbits a larger mass, due to the gravitational ‘pull’ of the larger mass
(Gravitational force acts as centripetal force)
What is the equation for the orbital speed of a satellite
v = √(GM/r)
Centripetal force of orbit is caused by force of attraction due to gravity
∴ F = m(v^2)/r = GMm/(r^2)
∴ v = √(GM/r)
What is the relationship between the orbital speed and orbital radius of a satellite
v ∝ 1/√r
∴ The larger the radius, the slower the satellite will travel
What is the equation for the orbital period of a satellite
T = √(4(π^2)(r^3)/GM)
Speed = d/t (d=2πr, t=T)
∴ T = 2πr/v
v = √(GM/r)
∴ T√(GM/r) = 2πr
∴ (T^2)(GM/r) = 4(π^2)(r^2)
∴ T = √(4(π^2)(r^3)/GM)
What is the relationship between The orbital period and orbital radius of a satellite
T^2 ∝ r^3
∴ The larger the radius, slower the satellite will travel, so it will take longer to complete each orbit
What is the total energy of a satelite
Ek + GPE
Always remains constant
How does the total energy of a satellite remain constant in a circular orbit
The orbital speed and radius are both constant
∴ Ek and GPE are both constant
∴ Total energy remains constant
How does the total energy of a satellite remain constant in an elliptical orbit
As the orbital radius decreases, the speed will increase
(as v ∝ 1/√r)
∴ Ek increases as GPE decrease (and vice versa)
∴ Total energy remains constant
What is the escape velocity of a gravitational
The minimum speed an unpowered object needs to completely leave the gravitational field of a planet and not ‘fall’ back towards it due to gravitational attraction
What is the equation for the escape velocity of a gravitational field
v = √(2GM)/r
GPE at infinity (escape) = 0
∴ To escape the gravitational field:
loss of Ek = Gain in GPE (form negative close to surface)
∴ (1/2)mv^2 = GMm/r
∴ v = √(2GM)/r
What is a synchronous orbit
When the satellite has an orbital period equal to the rotational period of the object it is orbiting
(eg. Geostationary orbit)
What is a geostationary orbit
A type of synchronous orbit where the satellite always stays at the same point above the earth as it spins
- T = 24hrs
- r = 42000km (36,000km above the surface)
- Used for TV/communications
What is a low orbit satellite
Any satellite orbiting between 180 and 2000km above the surface
- Orbits over north and south poles
- Used for mapping, spying, weather, etc.
What are the benefits of Low orbit satellites
- Cheaper to launch
- Sees more detail on surface
- More satellites available for each task
- Needs less powerful transmitters
What is an electric field
The region around a charged object where it can attract or repel other charges
(opposite charges attract and like charges repel)
When are electric fields uniform
Between two parallel plates of opposite charges
How can uniform fields be used to determine the charge of a particle within them
- As a charged particle enters a uniform field (at 90 degrees), it feels a constant force parallel to the field lines
- The direction of the force depends on the charge of the particle
- The particle will move in a parabolic path, accelerating towards the oppositely charged plate
When are electric fields radial
Around point charges
What is the direction of an electric field (and ∴ the field lines)
+ → -
How can 2D electric field lines be mapped
Conducting paper:
- Paper connected in series circuit, and parallel voltmeter used to measure the pd across it
- Points on the paper with the same pd can be connected to show equipotentials
- Field lines can be drawn, perpendicular to the equipotentials
How can 3D electric field lines be mapped
Electrolytic tank:
- water tank placed in series circuit, containing dissolved ions (electrodes placed in tank)
- Parallel voltmeter used to find places in the water with the same pd
- Equipotentials, and therefore parallel field lines can be determined
What is Coulomb’s law
F = Qq/(4πεo(r^2))
F: Magnitude of the force (Negative for attractive force, positive for repulsive force)
εo : Permittivity of free space (8.85x10^-12)
(If not in air, substituted for ε of the material)
Q & q: The charges of the 2 points
r: The distance between the two points
What is the constant of Coulomb’s Law
1 / 4πεo
What is the permittivity of free space (εo)
8.85x10^-12 (Fm^-1)
Why can coulomb’s Law be described as an inverse square law
F ∝ 1/(r^2)
∴ The force becomes weaker at a greater distance
This is because Electric fields are radial:
- If a sphere is drawn around the point charge, radius r, all points on the sphere will experience the same force
- SA = 4π(r^2)
- ∴ x2 Radius, SA = 4π((2r)^2) = 4(4π(r^2))
- This means the surface area of the sphere increases by the square of the scale of the increase in r (SA ∝ r^2)
- The force ∝ 1/SA (field lines spread out)
- ∴F ∝ 1/(r^2)
What is the electric field strength (E)
The force per unit positive charge experienced by an object in the electric field
What is the equation for electric field strength in a uniform field
E = F/Q ΔV/d
(d=distance between charged plates)
(Force is a vector, pointing towards the positive charge, and is Constant in uniform fields)
What is the equation for electric field strength in a radial field
E = Q/(4πεo(r^2)) = ΔV/Δr
∴ Depends on the distance from the point charge
(Derived by dividing the force from Coulomb’s Law by q)
What is shown by the area under a graph of electric field strength against radius
Electric potential
What is electric potential (V)
The energy required to move a unit positive charge from infinity, to a point within the field.
(Jkg^-1)
What is absolute electric potential (V)
The electric potential energy that a unit positive charge would have at a certain point in the field
When is electric potential positive or negative
Electric potential at infinity = 0
∴ Negative for attractive forces (-Q)
∴ Positive for repulsive forces (+Q)
What is the equation for electric potential (in a radial field)
V = Q/(4πεor)
Energy to move the unit positive charge is equal to the work done
Work done = Force x distance
F = E = Q/(4πεo(r^2))
(q = 1, for unit positive charge)
d = r
∴ Er = (Q/(4πεo(r^2)))r
∴ W = Q/(4πεor)
∴ V = Q/(4πεor)
What is shown by the gradient of a graph of electric potential against radius
Gradient = E
(ΔV/Δr = E)
What is electric potential difference
The energy needed to move a unit positive charge between two points at different distances r from Q, in an electric field.
What is the equation for the electric potential difference (in a radial field)
ΔV = Q/(4πεoΔr) = ΔV2-ΔV1
Potential difference = initial potential - final potential
∴ ΔV = ΔV2-ΔV1
∴ ΔV = Q/(4πεoΔr)
What is the equation for work done in an electric field
ΔW = qΔV
(change in electric potential energy)
Work done = Force x distance
F = Qq/(4πεo(r^2))
d = Δr
∴ Fd = (Qq/(4πεo(r^2)))r
∴ ΔW = Qq/(4πεor)
ΔV = Q/(4πεoΔr)
∴ ΔW = qΔV
What is electric potential energy
The energy required to move a charge q from infinity, to a point within the field. (Electric potential of charge q)
What is the equation for the electric potential energy (in a radial field)
Ep = Qq/(4πεor)
Work done = qΔV
Energy required is equal to the work done
∴ Ep = qΔV
ΔV = Q/(4πεoΔr)
∴ Ep = Qq/(4πεor)
What is the equation for the electric potential energy (in a uniform field, between 2 parallel plate)
Ep = Work done to move between the plates
ΔW = qΔV
What are the main difference between gravitational and electric fields
- G-fields are always attractive, whereas e-fields can be attractive or repulsive depending on the charges
- At a subatomic level, g gravity can be ignored (due to small masses and distances), whereas e-fields are still important, as electrostatic forces are stronger than gravitational forces at these distances (electrostatic force counteracted by strong nuclear force)
