3.7 Fields and their consequences Flashcards
What is a force field?
An area in which an object experiences a non-contact force
How can a force field be represented?
- A vector, describing the direction of the force that would be exerted on the object, which allows the direction of the field to be deduced
- Field lines, where the distance between the field lines represents the strength of the force exerted by the field in that region
How are force fields formed?
During the interaction of masses, static charge or moving charges
How are gravitational fields formed?
During the interaction of masses
How are electric fields formed?
During the interaction of charges
What are the similarities between gravitational and electrostatic forces?
- Both follow an inverse square law
- Both use field lines to be represented
- Both have equipotential surfaces
What are the differences between gravitational and electrostatic forces?
- In gravitational fields, the force exerted is always attractive, while in electric fields the force can be either repulsive or attractive
- Electrostatic forces act on charges, while gravitational forces acts on masses
What is gravity?
The universal attractive force acting between all matter
What is Newton’s law of gravitation?
The magnitude of force between two masses is directly proportional to the product of the masses, and inversely proportional to the square of the distance between them
Describe a uniform gravitational field.
- Equally spaced parallel lines, with arrows pointing towards the surface
- The same gravitational force is exterted on a mass everywhere in the field
Describe a radial gravitational field.
- Equally spaced lines with arrows pointing towards the centre of the object
- Force exerted depends on position of object in field - as an object moves further away from the centre, the magnitude of the force decreases, as the distance between field lines increases
What is gravitational field strength?
The force per unit mass exerted by a gravitational field on an object
What is the difference between the gravitational field strength of a uniform field and a radial field?
It is constant in a uniform field, but varies in a radial field
What is the gravitational potential at a point?
The work done per unit mass required to move an object from infinity to a given point
What is the gravitational potential at infinity?
Zero
Why is gravitational potential always negative?
The gravitational potential at infinity is zero, and as an object moves from infinity to a point, energy is released as the gravitational potential energy is reduced, and the gravitational force is always attractive, so the system is always doing the work
What is gravitational potential difference?
The energy per unit mass needed to move an object between two points
What are equipotential surfaces?
Points of equal potential joined together, so the potential on the surface is constant everywhere
What is the gravitational potential difference when moving along an equipotential surface?
Zero, so no work is done
What is the relationship between gravitational potential and the distance between two objects?
The gravitational potential is inversely proportional to the distance between the centres of the two objects
What is the gradient of a V-r graph?
-g
What is Kepler’s 3rd law?
The square of the orbital period is directly proportional to the cube of the radius, T²/r³=k
How do you derive Kepler’s 3rd law?
Centripetal force = gravitational force to find v^2
v^2 = (2πr/T)^2 to find T^2 = (constant) r^3
What is the total energy of an orbiting satellite made up of?
Kinetic and potential energy
Why is the total energy of an orbiting satellite always constant?
If the height is decreased, its gravitational potential energy decreases, but it will travel at a higher speed, so kinetic energy increases, so total energy is always kept constant
What is escape velocity?
- The minimum velocity an object must travel at in order to escape the gravitational field at the surface of a mass
- The velocity at which the object’s kinetic energy is equal to the magnitude of its gravitational energy
What are synchronous orbits?
Where the orbital period of the satellite is equal to the rotational period of the object it is orbiting (24 hours if orbiting Earth)
What are geostationary satellites?
Satellites that follow a specific geosynchronous orbit, their orbital period is 24 hours so they always stay above the same point on Earth, as they orbit directly above the equator
What are geostationary satellites used for?
Sending TV and telephone signals
What are low-orbit satellites?
Satellites that have lower orbits than geostationary satellites, so they travel much faster making their orbital periods much smaller
What are low-orbit satellites used for and why?
- Monitoring weather
- Making scientific observations about unreachable locations
- Military applications, spying
- They require less powerful transmitters and are able to orbit across the entire Earth’s surface
What is Coulomb’s law?
The magnitude of the force between two point charges in a vacuum is directly proportional to the product of their charges, and inversely proportional to the square of the distance between them
What is air treated as when using the force between two charges equation?
A vacuum
For a charged sphere, where is charge assumed to act?
At the centre of the sphere
What is the nature of the force if charges have the same sign?
Repulsive
What is the nature of the force if charges have different signs?
Attractive
Compare the magnitude of gravitational and electrostatic forces between subatomic particles.
The magnitude of electrostatic forces between subatomic particles is magnitudes greater than the magnitude of gravitational forces, because the masses of subatomic particles are incredibly small, whereas their charges are much larger
What is electric field strength?
The force per unit charge experienced by an object in an electric field
What is the general equation to find electric field strength?
E=F/Q
Derive the equation ΔW=QΔV.
W=Fd
F=EQ
E=ΔV/d, d=ΔV/E
W=(EQ)(ΔV/E), W=QΔV
What does the equation ΔW=QΔV represent?
The work done by moving a charged particle between the parallel plates of a uniform electric field
Describe the trajectory of a moving charged particle entering a uniform electric field initially at right angles.
The charged particle will experience a constant electric force either in or opposite to the direction of the field (depending on its charge), causing it to accelerate, so it follows a parabolic shape
What is absolute electric potential?
The potential energy per unit charge of a positive charge at a point in the electric field
Where is the absolute magnitude of electric potential greatest?
The surface of a charge
What is the electric potential at infinity?
Zero
What does the value of electric potential being positive or negative depend on?
The sign of the charge
What is the nature of the electric potential and charge if the charge is positive?
Electric potential is positive, and the charge is repulsive
What is the nature of the electric potential and charge if the charge is negative?
Electric potential is negative, and the charge is attractive
On a V-r graph, if V is initially positive, what is the nature of the force?
Repulsive
On a V-r graph, if V is initially negative, what is the nature of the force?
Attractive
What does the gradient of a V-r graph represent?
The value of electric field strength at that point
What is electric potential difference?
The energy needed to move a unit charge between two points
What does the area under an E-r graph represent?
Electric potential difference
What is capacitance?
The charge stored by a capacitor per unit potential difference
What is a capacitor?
An electric component which stores charge
What does a capacitor consist of?
Two conducting parallel plates with a gap between which may be separated by a dielectric (insulating material)
What happens when a capacitor is connected to a source of power?
Opposite charges build up on the two parallel plates causing a uniform electric field to be formed
What is permittivity?
A measure of the ability to store an electric field in a material, a property of dielectrics
How do you find relative permittivity?
By finding the ratio of the permittivity of the dielectric to the permittivity of free space, εr= ε/ε0
What is relative permittivity?
The dielectric constant of a dielectric, used to calculate the capacitance of a capacitor
What is a dielectric formed of?
Polar molecules
What are polar molecules?
Molecules with one end which is positive and one which is negative
How are polar molecules arranged when there is no electric field?
In random directions
What happens to polar molecules when an electric field is present in a capacitor?
- They move and align themselves with the field, with the negative ends rotated towards the positive plate of the capacitor and the positive ends to the negative plate
- Each molecule now has its own electric field, which now oppose the field formed by the capacitor, reducing this field
What does the electric field strength of a polar molecule depend on?
The dielectric’s permittivity
What happens as a result of polar molecules reducing the electric field formed by the capacitor?
The electric field strength decreases, decreasing the potential difference required to charge the capacitor, causing capacitance to increase, as C=Q/V
What does the area under a graph of charge against potential difference (Q-V graph) represent?
The electrical energy stored by a capacitor
What does a Q-V graph of a capacitor look like?
A straight line through the origin, as potential difference is directly proportional to charge
Describe a circuit in which you can charge a capacitor and take relevant measurements.
A series circuit with a power supply, ammeter, resistor and a capacitor, with a voltmeter in parallel with the capacitor
What does the area under an I-t graph represent?
Charge
What does the gradient of a Q-t graph represent?
Current
Describe what happens in a capacitor once it has been connected to a power supply.
- Current starts to flow and negative charge builds up on the plate connected to the negative terminal
- On the opposite plate, electrons are repelled by the negative charge building up on the initial plate, so these electrons move to the positive terminal
- An equal but opposite charge is formed on each plate, creating a potential difference
- As the charge across the plates increases, the potential difference increases but the electron flow decreases due to the force of electrostatic repulsion also increasing, so current decreases and eventually reaches zero
How do you discharge a capacitor?
It must be connected to a closed circuit with just a resistor
Describe the I-t graph of a charging capacitor.
Negative exponential curve, with current tending to zero
Describe the V-t graph of a charging capacitor.
Positive exponential curve, with potential difference tending to V0
Describe the Q-t graph of a charging capacitor.
Positive exponential curve, with charge tending to Q0
Describe the I-t graph of a discharging capacitor.
Negative exponential curve, with current tending to zero
Describe the V-t graph of a discharging capacitor.
Negative exponential curve, with potential difference tending to zero
Describe the Q-t graph of a discharging capacitor.
Negative exponential curve, with charge tending to zero
What happens when a capacitor is discharged?
Current flows in the opposite direction, and the current, charge and potential difference across the capacitor will fall exponentially, so it will take the same time for the values to halve
What is the equation involving current for a charging capacitor?
I = I0e^-t/RC
What is the equation involving current for a discharging capacitor?
I = I0e^-t/RC
What is the equation involving potential difference for a charging capacitor?
V = V0(1 - e^-t/RC)
What is the equation involving potential difference for a discharging capacitor?
V = V0e^-t/RC
What is the equation involving charge for a charging capacitor?
Q = Q0(1 - e^-t/RC)
What is the equation involving charge for a discharging capacitor?
Q = Q0e^-t/RC
What is I0?
The initial current
What is V0?
The initial potential difference
What is Q0?
The initial charge
What is the time constant?
- The product of resistance and capacitance, RC
- The value of time taken to discharge a capacitor to 1/e of its initial value of Q, I or V
- The value of time taken to charge a capacitor to (1 - 1/e) of its initial value of Q or V
What is the gradient of a graph of ln(Q) against t?
-1/RC
What is the time to halve, T1/2?
- The time taken for the current, charge or potential difference of a capacitor to discharge to half of the initial value
- T1/2 = -ln0.5RC = 0.69RC
What is induced when a current passes through a wire?
A magnetic field
What do the magnetic field lines induced by current passing through a wire form?
Concentric rings
How can the direction of the magnetic field around a current carrying wire be determined?
The right hand grip rule
What is magnetic flux density (B)?
A measure of the strength of a magnetic field, T
What is one Tesla?
A force of 1N on 1m of wire carrying 1A of current perpendicular to a magnetic field
What happens when a current-carrying wire is placed in a magnetic field?
A force is exerted on the wire
When is no force exerted on a current-carrying wire in a magnetic field?
If the current is travelling parallel to the magnetic field, because no component of the field is perpendicular to the current.
What is the formula for the force on a current-carrying wire in a magnetic field when the field in perpendicular to the current?
F = BIl
How can the direction of the force exerted on a current-carrying wire in a magnetic field be determined?
Fleming’s left hand rule
What is Fleming’s left hand rule?
- Thumb - represents the direction of the motion
- First finger - represents the direction of the field
- Second finger - represents the direction of the conventional current
What is the direction of a magnetic field on a magnet?
Arrows on field lines point from the North Pole to the South Pole.
What is the formula for the force acting on a moving charged particle in a magnetic field when the field is perpendicular to velocity?
F = BQv
How can the direction of the force on a moving charged particle in a magnetic field be determined?
Fleming’s left hand rule, where the second finger represents the direction of travel (v), and if the particle is negatively charged, the direction of the second finger must be reversed.
How does the force exerted on a moving charged particle in a magnetic field cause the particle to move?
The charged particle follows a circular path
Why do moving charged particles in a magnetic field follow a circular path?
The force exerted is always perpendicular to the motion of travel, acting as a centripetal force.
How can the radius of a moving charged particle’s circular path in a magnetic field be found?
r = mv/BQ
