This is the topic: 3.7 Fields and their Consequences for the AQA A-Level (and AS-Level) Physics course (from 2017 onwards). I got 4 A*s in my A-Levels (Physics, Maths, Further Maths, Computer Science), so they are very detailed and cover all of the specification for this topic.
Force Field = A region in which a body experiences a non-contact force.
Force is a vector, so a force field can be represented as a vector. Every point in the field can be given
a size and direction:
The direction of the vector shows the direction of the force that would be exerted on that
body if it was placed in that position in the field.
The direction of a force is shown by field lines, represented by arrows.
An object can be regarded as a point mass when it covers a very large distance as compared
to its size, so to study its motion, its size or dimensions can be neglected (which is why
planets can be treated as point masses).
Force fields arise from the interactions between bodies or particles:
Static or moving charged particles experience a force in an electric field.
Moving charged particles experience a force in a magnetic field.
Particles with mass experience a force in a gravitational field.
3.7.2. Gravitational Fields
Newton’s Law:
The force due to gravity, weight, is a universal force of attraction between all matter with mass. It is
an attractive force only. The gravitational force between two bodies is defined by Newton’s Law of
Gravitation:
Newton’s Law of Gravitation = The gravitational force between two point masses is proportional to
the product of their masses and inversely proportional to the square of the distance between them.
F = gravitational force between two masses (N)
m1, m2 = two different point masses (kg)
G = Newton’s gravitational constant (6.67x10 -11 Nm2kg-2) --> In data sheet
r = distance between the centres of the two masses (m)
This relationship: F ∝ 1/r2 is called the inverse square law. Although planets aren’t point masses, their radius is
relatively small compared to their separation, so they can
be treated as point masses.
--> When finding r, we add the radius of both planets
involved as the distance is from the centre of each.
Gravitational Field Strength:
Gravitational Field = A region where a mass experiences a force due to the gravitational attraction of
another mass. The direction of the gravitational field is always towards the centre of mass.
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,Gravity has an infinite range, so all objects with mass are affected. However, there’s a greater
gravitational force around objects with a large mass (e.g. planets), and a smaller force around
objects with a small mass (e.g. it is almost negligible for atoms).
Gravitational Field Lines:
These represent the direction of a gravitational field and point in the direction that a test mass
would accelerate if placed upon the line.
The field lines around a point mass are radially inwards.
Radial fields are non-uniform fields as the gravitational
field strength (g) is different depending on how far
away an object is from the centre of mass of the
sphere.
They begin at infinity and end on masses.
The gravitational field lines of a uniform field is
represented by equally spaced parallel lines. For
example, on the Earth’s surface, technically the lines
are at slightly different angles to each other, but due to
Earth’s size, on the surface they appear parallel.
A uniform sphere is one where its mass is distributed evenly, so the gravitational field lines around a
uniform sphere are identical to those around a point mass.
Gravitational Field Strength = The force per unit mass exerted on a small test mass placed at that
point. It is a measure of the density of field lines. It is a vector.
g = gravitational field strength (Nkg-1)
F = force due to gravity (N)
m = mass (kg)
If we imagine a test mass of mass 1kg in a
g = gravitational field strength (Nkg-1) This is only an equation for g for a radial field.
G = Newton’s gravitational constant
M = mass of the body producing the gravitational field (kg)
gravitational r = distance from the mass where you are calculating the field strength
field, we get
F = G(M x 1)/r2, so as g = F/1:
g also obeys the inverse square law:
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, Gravitational Potential:
Gravitational Potential Energy = The energy an object possesses due to its position in a gravitational
field.
We define that a system has zero potential energy when it is at infinity distance to that point.
Gravitational Potential = Gravitational potential at a point is the work done per unit mass in bringing
a test mass from infinity to a defined point. It is a scalar.
V = gravitational potential (Jkg-1)
G = Newton’s gravitational constant
M = mass of the body producing the gravitational field (kg)
r = distance from the centre of the mass to the point mass (m)
Gravitational
potential is always negative because:
The potential when the distance from the
mass is infinity is defined as 0.
Work must be done against the gravitational
pull of a planet to move a mass away from
it, so potential increases the further away
the mass is (more energy is required).
Two objects at the same point from a mass have the
same gravitational potential but may have different gravitational potential energies.
Two points at different distances from the mass will have different gravitational potentials, so there
will be a gravitational potential difference (ΔV) between them.
--> Gravitational potential difference is (final V – initial V).
Gravitational field strength is also known as the potential gradient (how quickly the
potential changes):
g = gravitational field strength (Nkg-1)
ΔV = change in gravitational potential (Jkg -1)
Δr = change in distance from the centre of a point mass (m)
V against r:
This uses V = -GM/r: As r increases, V follows a -1/r relation.
As V = -gr, the gradient is g. To find this use a tangent.
The graph has a shallow increase as r increases.
All values of V are negative.
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