Gravitational and electric fields Flashcards
+ magnetic field lines
Attractions
- opposite charges attract (-F)
- like charges repel (+F)
Coulomb’s law
The force of attraction or repulsion
between two point charges is directly
proportional to the product of the two
charges and inversely proportional to the
square of the distance between them.
F = k(q1q2/r2)
F - electrostatic force
q1 - object 1 charge
q2 - object 2 charge
r - separation distance
k - coulomb’s constant
k = 1/(4pipermittivity of free space)
Quantifying charge
The total charge in Coulombs can be
related to the number of electrons
- elementary charge (e) in the data booklet
- metric prefixes important
Gravity
All mass attracts all other mass
The universal law of gravitation
The force of attraction between bodies
with mass is directly proportional to the
product of the two masses and inversely
proportional to the square of the
distance between them.
F = G(m1m2/r2)
F - gravitational force [N]
m1 - object 1 mass [kg]
m2 - object 2 mass
r - separation distance [m]
G - gravitational constant [Nm2kg-2]
Permittivity
Permittivity changes relative to the substance
er = e/eo
*IB might ask you about
this: the higher the
relative permittivity, the
harder it is for
electrostatic forces to
travel over a distance…
Field lines, gravitational F
Field lines show the direction that a force would act on a test object, test mass in this case
- Field lines closer together imply a larger force than
field lines further apart
Kepler’s first law
The orbit of a planet is an ellipse with the
Sun at one of the two foci.
A circle is a special case of an ellipse
where both foci are coincident.
Most planetary orbits are almost circular
with low eccentricity.
Eccentricity is a measure of how much
an ellipse deviates from a circle.
Kepler’s second law
A line segment joining a planet and the
Sun sweeps out equal areas during equal
intervals of time.
This law implies that a planet moves faster
when it is closer to the Sun and slower
when it is farther away.
The point of closest approach to the Sun is
called the perihelion, and the point of
farthest approach is called the aphelion.
This law applies to all orbiting bodies,
including comets and asteroids.
Kepler’s third law
T2/r3 = (4pi2)/GM
T2 = ((4pi2)/GM)a3
T - earth years
a - astronomical units (a = 1AU for Earth)
M - solar masses
then (4*pi2)/G = 1
***might need to derive this
Conditions under which extended bodies can be treated as body masses
Uniform Spherical Bodies (Outside the Body)
- A spherically symmetric body (e.g., a planet or star with uniform density) can be treated as a point mass located at its center of mass when calculating the gravitational field outside the body. This follows from Newton’s Shell Theorem, which states that a uniform spherical mass exerts the same gravitational force as if all its mass were concentrated at a single point at the center.
Small Distance Relative to Size
- If the size of the object is much smaller than the distances involved in the problem (e.g., a spacecraft orbiting Earth), then the object’s mass can be considered concentrated at a point.
Internal Gravitational Fields (Within a Uniform Sphere)
- Inside a uniform spherical body, the gravitational force at a given radius depends only on the mass enclosed within that radius.
The object still behaves as if the enclosed mass were concentrated at the center.
Negligible Rotational Effects
- If rotational motion and internal mass distribution (e.g., tidal effects) are insignificant, the object can be approximated as a point mass.
Far-Field Approximation
- When observing the gravitational effects of an extended body from a large distance, the variations in mass distribution become negligible, allowing the body to be treated as a single mass at its center.
Explain why a centripetal force is needed for the planet to be in a circular orbit
circular motion involves a changing velocity;
Tangential velocity is always perpendicular to
centripetal force/acceleration; there must be a
force/acceleration toward center/star; without a
centripetal force, the planet will move in a straight
line
Gravitational field
a region where a mass experiences a force because of its mass
Uniform field (close to the Earth)
when a mass is always downwards in the same direction with the same force
Addition of fields
since field strength is a vector, when we add field strengths caused by several bodies, we MUST remember to add them vectorially.
Milikan’s oil drop experiment (where the knowledge of the fundamental charge comes from)
Milikan and Fletcher sprayed a fine mist of oil drops into a chamber, where they were ionized (adding or removing electrons) by X-rays that were passed through the nozzle. The charged oil drops were released into a region of uniform electric field. When no potential difference was applied across the plates, the oil would fall under gravity and reach terminal velocity when drag was the same as the gravitational force. When an upward electric force was applied, some drops (depending on their mass) would become stationary or rise upward with a new terminal velocity. The balance of forces enabled the charge on individual oil drops to be determined.
Although no single oil drop had the fundamental charge exactly, all charges found through this method shared a common factor: 1.60 × 10-19 C. This quantity of charge remains the smallest that has been found by any experimental procedure.
The conservation of electric charge
states that the total amount of electric charge in a closed system must remain constant.
- example: When a glass rod is rubbed against silk, the rod becomes positively charged whereas the silk does become negatively charged. This same number of positive ions on glass rod is discovered to be the same as the quantity of negative ions on silk.
Friction
The process of transferring charge between two objects by rubbing them together. Electrons move from one material to another, often causing one object to become positively charged and the other negatively charged.
Electrostatic induction
The redistribution of charges in a neutral object when a charged object is brought near it, causing one side to become oppositely charged while the other side retains a similar charge. No direct contact occurs.
By contact
A method of charging where a charged object touches a neutral object, allowing electrons to transfer and giving both objects similar charges.
Grounding (Earthing)
The process of removing excess charge from an object by connecting it to the Earth, which acts as a vast reservoir of charge and neutralizes the object.
Electric field
a region of space where an electric force is experienced
Field strength, E
The size of the field at a given point is given by the electric field strength.
- This is defined as the force per unit charge experienced by a small positive test charge placed at that point. So if we consider a point some distance from a sphere of positive charge, the field strength E would be E = F/q. Since force is a vector, field strength will also be a vector with the same direction as the force. The unit of field strength is N C-1. If the field strength at a point is E, a charge +q placed at that point will experience a force Eq in the direction of the field. A charge - q will experience the same size force but in the opposite direction.
Field lines, electric
Field lines are drawn to show the direction and magnitude of the field. So for a point positive charge, the field lines would be radial, showing that the force is always away from the charge. The fact that the force gets stronger as the distance from the charge decreases can be seen from the density of the lines.
- A point charge placed inside the sphere will experience forces in all directions due to each of the charges on the surface. The resultant of these forces is zero no matter where the point charge is placed. The electric field inside a charged sphere is therefore zero.
