Fields Flashcards
Similarities and Differences between Gravitational Fields and Electric Fields
Similarities:
- both have inverse-square laws
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Differences:
- masses always attract, charges can both attract and repel
What is a Force Field?
A region in which a body experiences a non-contact force
e.g the gravitational field
Field Lines
- field lines are lines of force
- ## field line directions are presented based on the positive charge, meaning they emanate out of positive charges and inwards for negative charges
State Newton’s Law of Gravitation
- The force of attraction between two point masses
- is proportional to the product of the two masses
- and inversely proportional to the square of the distances between them
F = GMm/r^2
What is g?
The strength of a gravitational field, g, is the force per unit mass in a small test mass placed in the field
and also the acceleration of a falling object when under freefall
What is Gravitational Potential Energy?
- the energy of an object due to its position in a gravitation field
What is the Gravitational Potentialv
The work done per unit mass to move a small object from infinity to that point
Equipotentials
What is a Potential Gradient?
- the potential gradient at a point in a gravitational field is the change of potential per metre at that point
- potential gradient = V/r (for small distances of r)
- gravitational field strength is the negative of the potential gradient
Escape Velocity (from a planet)
- the escape velocity from a planet is the minimum velocity an object must be given to escape from the planet when projected vertically from the surface
- if an object is projected at speed v
1/2mv^2 > ΔW
1/2mv^2 > GMm/R
so v^2 > 2GM/R
so escape v = (2GM/R)^1/2
g = GM/(R^2)
∴ Vesc = (2gR)^1/2
Why is the gravitational field strength linear from 0-R of the earths radius?
At the Earth’s center, g is zero. As the point goes away from the centre, the gravitational field strength increases in proportion to the distance.
where mass = density x volume
so enclosed mass = (4 /3)pir^3
Satellites
- Any large mass that orbits a larger mass is a satellite e.g the moon is a natural satellite of the earth
- Geostationary/Geosynchronous satellites orbit the earth directly above the equator
- this is because it has a time period of exactly 24HRS so if it had the same time period as the earth’s rotation
radius of orbit can be found r^3/T^2=GM/4π^2
- this is because it has a time period of exactly 24HRS so if it had the same time period as the earth’s rotation
- Polar Orbits
- low orbit
- the force of gravitational attraction between each planet and the sun is the centripetal force that keeps the planet on its orbit
- GM/r^2 = v^2/r where M is the mass of the sun
- v^2 = GM/r
- v = 2πr/T
- (2πr)^2/T^2 = GM/r
therefore
r^3/T^2 = GM/4π^2
and because GM/4π^2 is the same for all planets then r^3/T^2 is the same for all of the planets
KE = 1/2 mv^2 = 1/2mx GM/r = GMm/2r
V = -GM/r
Ep = mV = - GMm/r
= -GMm/r + GMm/2r = -GMm/2r
E = -GMm/2r
What is the Electric Field Strength?
- The force per unit charge on a positive test charge placed at that point
- units NC^1
- F= EQ
where E is field strength, F is force and Q is charge - the electric field strength is a before in the same direction as the force on a positive test charge
- uniform
- parallel to each other
- at right angles to the plates
- from the positive plate to the negative plate
The force in a small test charge in an electric field is…
- In the same direction as the electric field if the charge is positive
- In the opposite direction to the electric field if the charge is negative
Why must a test charge need to very much less than 1 Coulomb?
- this amount if charge would affect the charges that cause the field, and so it would alter the electric field and its field strength
- For a charged metal conductor, the charge on it is spread across its surface
- the more concentrated the charge is on the surface, the greater the strength of the electric field above the surface
Electric potential
- The work done per unit positive charge on a positive test charge when it is moved from infinity to that position in the field
where V = EPE/Q
- Equipotentials are surfaces of constant potential
- a test charge moving along an equipotential has constant potential energy
- no work is done by the electric field on the test charge because the force due to the field is at right angles to the equipotentials
Potential Gradients
- the potential gradient at any position in an electric field is the change in potential per unit charge of distance in a given direction
- the closer the equipotentials are the greater the potential gradient is (at right angles to the equipotentials)
- the electric field strength is equal to the negative of the potential gradient
- The gravitational potential in a gravitational field is always negative because it’s attractive
- the electric potential in the electric field near a point charge Q can be both positive or negative according to whether Q is a positive or negative charge
What is the Motor Effect?
- A current-carrying wire placed at a non-zero angle to the lines of force of an external magnetic field experiences a force due to the field
- The force is perpendicular to the wire and to the lines of force
- the magnitude of the force depends on:
- the current
- strength of the magnetic field
- the length of wire
- the force is:
- greatest when the wire is at right angles to the magnetic field
- zero when the wire is parallel to the magnetic field
Couple in a coil in a magnetic field
- each wire experiences BIl where l is the length of each long side
- each long side experience a horizontal force F = (BIl)n in the opposite directions at right angles to the field lines
- the pair of forces acting on the long sides form a couple as they are not directed along the same line
- the torque of the couple = Fd
- the beam follows a circular path because the direction of the force on each electron is perpendicular to the direction of motion of the electron (and field direction)
- The electrons moving along the current-carrying wire are pushed to one side by the force of the field
- the electrons being confined to a wire cause the whole wire to move downwards
- the force of the magnetic field on a moving charged particle is at right angles to the direction of motion of the particle
- No work is done by the magnetic field on the particle as the force always acts perpendicular to the velocity of the particle
- the kinetic energy of a particle is unchanged by the magnetic field
- the force causes a centripetal acceleration
-m
How can radius of curvature for a particle under a magnetic field be used to determine the particle
r = mv/BQ
- the larger the radius the greater the mass of the particle
- the smaller the charge the smaller the radius
How can you increase the induced EMF of a wire?
- move the wire faster
- use a stronger magnet
- make a wire into a coil
- pushing the magnet in or out of the coil
How to increase Efficiency of a transformer
- thick copper wire to reduce resistance due to wire
- EMF may be induced in the iron causing eddy currents which will resist the flow of charge and emit heat, laminate the layers to prevent it
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Len’s Law states
- the direction of the induced current is always such as to oppose the change that causes the current
Faraday again lawl
- law of electromagnetic induction states that the induced emf in a circuit is equal to the rate of change of flux linkage through the circuit
Loaded and Unloaded Motors
- An unloaded motor will spin with a high speed
- the rate of change of flux linkage is high so the induced back EMF will be high.
- there is small potential difference between the back EMF and EMF causing the motor to spin
- thus the resulting current is low
- The speed is limited by resistive forces (bearing friction and air resistance)
- little power used
Loaded Motors
- A loaded motor will spin with a low speed
- the rate of change of flux linkage is low
- induced back EMF will be low
- there is a large potential between the back EMF and the EMF
- causing the motor to spin and the resulting current is high
- Power is transferred from the voltage source to mechanical power in the load and wasted heat due to resistance
Len’s Law
- The induced/Back EMF will always oppose or tend to oppose the flux change produced
- When a magnet i pushed in to a coil the induced EMF opposes the motion by producing a field which repels the magnet
- when you remove the magnet from the coil the induced emf opposes this motion by producing a field that attracts the magnet
- in both case work must be done to move the magnet
- this work is what transfers energy to a component
Coil Attached to Oscilloscope (update)
- A magnet is dropped through a coil that is connected to an oscilloscope
in the case below:
the emf at A is smaller than the emf at C because the magnet will be moving faster ( because the magnet is being accelerated due to gravity), so more flux linkage cut
Faraday’s Law
- EMF is proportional to the rate of change of flux linkage
