FIELDS & THEIR CONSEQUENCES

Back Emf

An emf generated by the coil in an AC generator that acts against the potential difference that has been supplied to the motor.

Capacitance, C

The charge stored per unit pd in a capacitor.

Capacitor

An electrical component that stores charge. A parallel-plate capacitor is made of two parallel conducting plates with an insulator between them (dielectric).

Coulomb’s Law

The size of the force that acts between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation. It is attractive for opposite charges and repulsive for like charges.

Cyclotron

A particle accelerator made up of two D shaped electrodes positioned opposite each other. The electric field changes direction each time a particle moves from one electrode to the other, causing the particle to accelerate.

Dielectric

An insulating material placed between the two plates of a capacitor in order to increase the amount of charge it can store.

Electrical Conductor

A material that contains free electrons that are able to move throughout the material and carry charge.

Electrical Insulator

A material that does not contain any free electrons. All electrons in an insulator are part of the individual atoms that make it up.

Electric Field

A region surrounding a charged object which causes a force to be exerted on any charged object placed within the field.

Electric Field Strength, E (at a point in the field)

The force per unit positive charge exerted on a charged object placed at that point in the field. This is a vector acting in the same direction as the force on a positive charge.

Electric Potential, V (at a point in the field)

the work done per unit charge on a positive test charge in bringing it from infinity to that point in the field.

Electromagnetic Induction

When an emf is induced in a wire/conducting rod when it is moved relative to a magnetic field.

Equipotential

A surface of constant potential. No work is done by the field when an object moves along an equipotential.

Escape Velocity

The minimum velocity required by an object to be able to escape a gravitational field of a mass when projected vertically from its surface.

Faraday’s Law

The magnitude of the induced emf is equal to the rate of change of flux linkage through the circuit.

Field Line / Line of Force

A line representing the path that a north pole (magnetic field), positive charge (electric field) or mass (gravitational field) would take when placed within the field.

Force Field

An area in which an object will experience a non-contact force.

Geostationary Satellite

A satellite that orbits above the equator with a 24 hour period, so it will always remain above the same position on the Earth. They orbit approximately 36,000 km above the surface of the Earth.

Gravitational Field

A region surrounding a mass in which any other object with mass will experience an attractive force.

Gravitational Field Strength

The force per unit mass exerted on a small test mass placed

within the field.

Gravitational Potential, V (at a point in the field)

The work done per unit mass required to move a small test mass from infinity to that point.

Gravitational Potential Energy

The component of an object’s energy due to its position in a gravitational field.

Kepler’s Third Law

The square of an object’s orbital period (T) is directly proportional to the cube of its orbital radius (r) – T^2 ∝ r^3.

Lenz’s Law

An induced current is always in a direction so as to oppose the change that caused it.

Magnetic Field

A region surrounding a magnet or current-carrying wire that will exert a force on any other magnet or current-carrying wire placed within it.

Magnetic Flux, ϕ

A value which describes the magnetic field or field lines passing through an area. It is the product of magnetic flux density and the perpendicular area it passes through.

Magnetic Flux Density, B

The force per unit current per unit length on a current-carrying wire placed at 90º to the field lines. Sometimes also referred to as the magnetic field strength.

Magnetic Flux Linkage, Nϕ

The magnetic flux multiplied by the number of turns, N, of the coil.

Motor Effect

When a current-carrying wire is placed within a magnetic field (non-parallel to the field lines) and experiences a force perpendicular to both the wire and the field lines.

Permittivity of free space, ε_0

A measure of the ability of a vacuum to allow an electric field to pass through it.

Polarised

An atom/molecule becomes polarised when an external electric field causes the negative electron cloud to be shifted in the opposite direction to the positive nucleus – the charges are pulled in opposite directions. (This is what happens to the molecules of the dielectric in a capacitor).

Potential Gradient

The change of potential per metre at a point in the field.

Radial Field

A field in which the field lines are all directed towards a single point (e.g. the centre of a planet or a point charge).

Relative Permittivity

The ratio of charge stored in a capacitor with the dielectric to charge stored without the dielectric. Also sometimes referred to as the dielectric constant.

Step-down Transformer

A device made of two insulated wires coiled around an iron core in which the output voltage is smaller than the input voltage due to the secondary coil having fewer turns than the primary coil.

Step-up Transformer

A device made of two insulated wires coiled around an iron core in which the output voltage is greater than the input voltage due to the secondary coil having more turns than the primary coil.

Synchronous Orbit

An orbit in which the period of the orbit is equal to the rotational period of the object that it is orbiting.

Time Constant

The time taken for a capacitor to discharge to 37% (e^-1) of its initial charge. The time constant is equal to the product of the capacitance and the resistance of the fixed resistor (that the capacitor is being discharged through).

Uniform Field

A field in which all of the field lines are parallel and equally spaced – field strength is equal in all areas of the field.

Force field

A force field is an area in which an object experiences a non-contact force.

Different types of fields are formed depending on which interaction takes place.

1. Gravitational fields

2. Electric fields

Gravitational fields

Formed during the interaction of masses.

Electric fields

Formed during the interaction of charges

Gravity

Acts on any objects which have mass and is always attractive.

Gravitational field strength (g)

Gravitational field strength (g) is the force per unit mass exerted by a gravitational field on an object. This value is constant in a uniform field, but varies in a radial field.

Gravitational potential (V)

Gravitational potential (V) at a point is the work done per unit mass when moving an object from infinity to that point.

Gravitational potential difference

The gravitational potential difference (ΔV ) is the energy needed to move a unit mass between two points and therefore can be used to find the work done when moving an object in a gravitational field.

Equipotential surfaces

Equipotential surfaces are surfaces which are created through joining points of equal potential together, therefore the potential on an equipotential surface is constant everywhere.

Total energy

The total energy of an orbiting satellite is made up of its kinetic and potential energy, and is constant.

Total energy of a satellite = kinetic energy + potential energy

Geostationary satellites

Geostationary satellites follow a specific geosynchronous orbit, meaning their orbital period is 24 hours and they always stay above the same point on the Earth, because they orbit directly above the equator.

Low-orbit satellites

Low-orbit satellites have significantly lower orbits in comparison to geostationary satellites, therefore they travel much faster meaning their orbital periods are much smaller.

Coulomb’s law

Coulomb’s law states that 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 the charges.

Electric field strength (E)

Electric field strength (E) is the force per unit charge experienced by an object in an electric field. This value is constant in a uniform field, but varies in a radial field.

Electric potential difference

Electric potential difference (ΔV) is the energy needed to move a unit charge between two points. Therefore, the work done (ΔW) in moving a charge across a potential difference is equal to the product of potential difference and charge.

ΔW = QΔV

Capacitance (C)

Capacitance (C) is the charge stored (Q) by a capacitor per unit potential difference (V).

C = Q/V

Capacitor

A capacitor is an electrical component which stores charge.

Two types of transformer.

1. Step-up transformer

2. Step-down transformer

Step-up transformer

Increases the input voltage by having more turns on the secondary coil than the primary.

Step-down transformer

Decreases the input voltage by having less turns on the secondary coil.

The force felt in a force field is a non-contact force. True or False?

True.

Is force a vector or scalar quantity?

A vector.

What are some similarities between electrostatic and gravitational forces?

● Inverse square force laws

● Potential concept

● Equipotential surfaces

● Use of field lines

What are some differences between electrostatic and gravitational forces?

The gravitational forces from masses always attract, whilst charges may repel or attract.

What is gravity?

Gravity is the universal attractive force which acts between all matter.

What is G?

The universal gravitational constant.

Approximately 6.67 x 10¯¹¹ m³ • kg¯¹ • s¯²

What can field lines tell you about a field?

The direction of the field and the strength of the field depending on the density of the field lines.

What is 𝘨?

𝘨 is the force per unit area in a uniform field. In a radial field the magnitude of 𝘨 is the the proportionality constant at that point between force and mass.

Iet 𝘨 = G•M/r²

What is gravitational potential?

The potential energy per kilogram, at any point in the field. 0 potential is defined at infinity, hence at a point close to a mass the potential of an object would be negative.

What is the work done by moving a mass in a field?

Mass x change in potential

What is the gravitational potential difference?

Gravitational potential difference is the difference in the gravitational potentials of two points in a gravitational field.

What is an equipotential surface?

A surface in which every point on the surface has the same potential.

How much work is done when you move 1 km in any direction on an equipotential?

No work is done when moving across equipotentials, as the potential at each point is the same.

Why is gravitational potential a negative value?

Work needs to be done to move an object from the inside the field to outside the field. Since outside the field’s potential is defined as 0 then the potential inside the field must be negative.

How is the orbital period related to the radius of a circular orbit?

T² ∝ R³

What equations could one use to find the speed of an orbiting satellite?

The orbiting object (mass m) is in circular motion, so we would use F = ma with F = GMm/r^2 rearranged to a = v^2 / r = ω^2/r. This can be sold to find the speed (v), angular speed (ω), the radius of the orbit or using T = 2π/ω its period.

Compare the PE and KE of a lower orbit to a higher one.

A lower orbit (smaller m) has less potential energy and more kinetic energy than a higher orbit (bigger r).

What is the period of a geosynchronous orbit?

Geosynchronous orbits have a period of one day.

How is capacitance calculated?

C = Q \ V

where:

C is Capacitance (F)

Q is Charge in the plates (C )

V is potential difference across the plates (V)

What is the relative permittivity (a.k.a. dielectric constant)?

● The ratio of the charge stored with the dielectric between the plates to the charge stored when the dielectric is not present.

● ε_r = Q / Q_0

● The greater the relative permittivity, the greater the capacitance of the capacitor.

What does the area under the graph of charge against pd represent ?

The energy stored by the capacitor.

What is the half time of a capacitor?

T½ = 0.69RC

How does a capacitor charge up?

1. Electrons move from negative to positive around the circuit.

2. The electrons are deposited on plate A, making it negatively charged.

3. Electrons travel from plate B to the positive terminal of the battery, giving the plate a positive charge.

4. Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates.

5. When the p.d across plates = source p.d., the capacitor is fully charged and current stops flowing.

Describe and explain in terms of the movement of electrons how the p.d across a capacitor changes, when it discharges across a resistor.

1. Electrons move in opposite direction than when the capacitor was charging up.

2. Charge on one plate A decreases as it loses electrons, and plate B gains electrons, neutralising them.

3. P.d. decreases exponentially across the plates.

State the 3 expressions for the energy stored by a capacitor.

E = ½ (Q^2 /C) = ½ (QV) = ½ (CV^2 )

What 2 factors affect the time taken for a capacitor to charge or discharge?

● The capacitance of the capacitor, C. This affects the amount of charge that can be stored by the capacitors at any given potential difference across it.

● The resistance of the circuit, R. This affects the current in the circuit and how quickly it flows, hence how quickly the capacitor charges/discharges.

What symbol represents the permittivity

of free space?

𝜀₀

When calculating the force between two particles, what can air can be treated as?

A vacuum.

For a charged sphere the charge can be assumed to be at what part of the sphere?

The centre.

Which is stronger? The gravitational force of subatomic particles or the electrostatic force.

The electrostatic force.

Electric field lines always go from _____ to _____.

Electric field lines always go from positive charge to negative charge.

What is electric field strength?

The force per unit charge acting at a point in an electric field.

What is the magnitude of E (electric field strength) in an uniform electric field?

Potential difference between plates (V)/distance between plates.

What is the trajectory of a particle entering a uniform field at right angles?

It is parabolic.

How is electric potential related to electric field strength?

E = ΔV/Δr

The change in electric potential with respects to the change in radius length.

When a magnetic field is perpendicular to a current-carrying wire, does the wire feel a force?

Yes, the magnitude of the force is = BIl.

Where:

l is length of the wire

B is Magnetic flux density

I is Current in the wire

Fleming's left hand rule for motors represents what properties on what fingers?

Thumb - Thrust/Force

First finger - Field (Magnetic)

Second finger - Current

What is magnetic flux density (B)?

Flux density measured in Tesla (T) or Webers/metres² (Wb/m²), is the flux per metre².

A charged particle moving through a field feels a force when it is traveling along the field lines or perpendicular to them?

Perpendicular to the field.

What is the equation for the Force felt by a moving charge in a magnetic field?

F = BQv

Is the force applied to the particles applied perpendicular to the particles motion or in one direction?

Perpendicular to its motion, causing it to move in a circular motion.