Gravitational and Electric Fields (Unit 4) Flashcards
Newton’s Law of Gravity
an attractive force between two point masses
proportional to the product of their masses and inversely proportional to their separation squared
Concept of a force field
the region in which a body experiences a force
Representation of gravitational field lines (radial and uniform fields)
See sheet
Equipotential
Line joining points of equal potential
No work is done moving an object along an equipotential
Gravitational field strength, g
the force acting per unit mass
Gravitational field strength units
N kg-1 VECTOR
Gravitational potential, V, (at a point)
work done per unit mass to move a small mass from infinity to that point.
Units of gravitational potential
J kg-1 SCALAR
Gravitational potential, V, at infinity
zero
Gravitational potential difference, V, between two points
work done per unit mass to move a small mass from one point to the other.
Graphical variation of magnitude of g with r
See sheet
Graphical variation of V with r
See sheet
Area under graph of gravitational field strength against r
work done moving a unit mass between the two points
Gradient of graph of gravitational potential against r
gradient = -g (gravitational field strength); g= -(deltaV/delta r)
Derivation of Kepler’s Law
- Gravitational force = centripetal force
- GMm/r2 = mv2/r or GMm/r2 = mr(omega)2
- substitute for v (v = (2pi x r)/T) or omega( omega = (2pi)/T)
- re-arrange to get T2 = ((4pi2)/GM) x r3
Energy considerations of an orbiting satellite
Total satellite energy = kinetic energy + grav. potential energy
Total satellite energy = 1/2mv2 - GMm/r
Features of a geosynchronous orbit
- orbits over equator
- maintains a fixed position relative to surface of Earth
- period is 24 hours (same as the Earth)
- offers uninterrupted communication between transmitter and receiver
- steerable dish is unnecessary
Escape velocity of an object from a planet
loss of kinetic energy = gain in grav. potential energy
(to get to infinity, need to provide grav. potential energy)
= 1/2mv(escape)2 - GMm/r
gives v(escape) = Square root of 2GM/r
Coulomb’s Law
magnitude of force between two point charges
is proportional to the product of their charge and inversely proportional to their separation squared
the force is ATTRACTIVE with un-like charges and REPULSIVE with like charges.
Representations of electric field lines
See sheet
Electric field strength, E
force acting per unit charge on a positive charge.
Electric field strength units
N C-1 or V m-1 VECTOR
Electric potential, V, (at a point)
work done to move a small unit positive charge from infinity to the point
Units of electric potential, V
J C-1 or V (Volts) SCALAR
Electric potential, V, at infinity
Zero
Electric potential difference, V, between two points
work done to move a small unit positive charge from one point to the other.
Graphical variations of E with r (radial and uniform fields)
See sheet
Graphical variations of V with r (radial and uniform fields)
See sheet
Area under graph of electric field strength against r
See sheet
Path of charged particle in a uniform electric field
Path is parabolic, because,
Magnitude of force is constant and always in the same direction
Speed of charged particle accelerated across a potential difference, V
Loss of electrical potential energy = gain in kinetic energy
QV = 1/2mv2
Similarities between electric and gravitational fields
field strengths are both inversely proportional to separation squared
potentials are both inversely proportional to separation
(see table on Pg 89 of A2 text book.)
Differences between electric and gravitational fields
masses always attract but charges may attract or repel
see table on Pg 89 of A2 text book
