Fields Flashcards
Gravitational fields definition
a region of space where an object experiences a force because of its mass
Gravitational field strength definition
the force per unit mass experienced by a small point test mass placed in the field
Electrostatic field definition
a region of space where an object experiences a force because of its charge
Electrostatic field strength definition
the force per unit charge experienced by a small positive test charge placed in the field
Gravitational potential energy definition
of a mass placed at a point can be defined as the work done in moving it from infinity to that point (regardless of the path taken) (J)
Gravitational potential definition
the work done in taking a unit mass from infinity to that point (Jkg-1)
Equipotential lines
drawn at 90 degrees to field lines
Escape speed definition
the speed of a body needs to escape the gravitational attraction of a planet (i.e. to reach an infinite distance away) from the surface of the planet
deriving the Vesc formula
at the planet’s surface, the body has a gravitational potential energy equal to
Ep=(-GMm)/r
For a body of mass to escape it must reach an infinite distance away where Ep=0
It must gain (GMm)/r of energy. This energy is in the form of kinetic energy so:
1/2m(Vesc)^2 = (GMm)/r
(Vesc)^2 = (2GM)/r
Vesc √((2GM)/r)
Deriving the Vorbit formula
satellites orbiting an object are undergoing circular motion with the gravitational attraction of the object they are orbiting providing the centripetal force
gravitational attraction = centripetal force
(GMm)/r^2 = (mVorbit^2)/r
Vorbit = √((GM)/r)
Deriving total energy of satellites
a satellite will have both Ek and gravitational Ep
Ek = 1/2mv^2 but v=√((GM)/r)
so Ek = 1/2 (GMn)/r
Ep = -(GMn)/2
so the total energy = Ek + Ep = 1/2 (GMm)/r - (GMm)/r
= -1/2 (GMm)/r
therefore the total energy is negative
Energy changes as a satellite moves from a lower to higher orbit
the total energy becomes less negative
Ek decreases as r increases (V=√((GM)/r)
Ep increases as r increases (i.e gets less negative)
Electric potential (Ve) definition
work done per unit charge in brining a small positive test charge from infinity to that point (units JC-1or V)
Type of motion that a charged particle undergoes when enters a magnetic field
the force of the particle is at 90 degrees and so it undergoes circular motion
* the charge must be moving
Type of motion that a charged particle undergoes when enters a electric field
the force will be parallel to the field lines
therefore the particle undergoes parabolic motion
* charge may be stationary or moving to experience a force
