Fields and their consequences

What is a force field?

Area in which an object experiences a non-contact force

How does the field strength change with distance?

Inverse square law/Strength quarters when distance halves

What is an equipotential?

Lines of equal potential surrounding an object of a field.

Newton’s law of gravitation

The magnitude of a force between two masses is directly proportional to the product of the masses, and is inversely proportional to the square of the distance between them/ F = Gm₁m₂/r²

Uniform field

A field that exerts the same force on an object wherever it is in the field

Radial field

A field where the force exerted depends on the position of the object in the field

Gravitational field strength

The force per unit mass exerted by a gravitational field on an object

Gravitational potential

The work done per unit mass against gravity to move an object from infinity to a given point in the field

Gravitational potential difference

The energy needed to move a unit mass between two points in a gravitational field

Equipotential surfaces

Surfaces which are created by the joining of equipotential points

Kepler’s third law

Square of the orbital period is directly proportional to the cube of the radius/T² ∝ r³

How to derive Kepler’s 3^rd law

Equate centripetal force and gravitational force/ mv²/r = GM/r²

Total energy of a satellite

Kinetic energy + Potential energy

Escape velocity

The minimum velocity an object must travel at in order to escape the gravitational field at the surface of a mass

Synchronous orbit

When the orbital period of a satellite is the same as the period of the object that it is orbiting

Geostationary satellite

A satellite that has a synchronous orbit and always stay above the same point on the body they orbit around

What happens to linear speed when a satellite orbit has a smaller radius

It increases

Coloumb’s law

The magnitude of the force between two point charges is directly proportional to the product of their charges and is inversely proportional to the square of the distance between the charges/F = Q₁Q₂/4πϵ₀ r²

Permittivity

The ability of a medium to store electrical charge

Electric field strength

The force per unit charge experienced by a positive test charge in an electric field

Which direction do field lines point from a positive charge?

Away

Which direction do field lines point from a negative charge?

Towards

Electric potential

The potential energy per unit charge of a positive test charge at a certain point in a field

Electric potential difference

The energy needed to move a unit charge between two points

Capacitance

Capacitance is the charge stored by a capacitor per unit potential difference

What is a capacitor?

An electrical component that stores charge

Dielectric

The insulating material found between the parallel plates in a capacitor

How does a capacitor work?

When connected to a power source, opposite charges build up on the two parallel plates, which cause a uniform electric field to be created

Dielectric constant

ϵ_r = ϵ/ϵ₀

Capacitance formula

Proportional to the area of the plates, inversely proportional to the distance with a constant of ϵ₀ϵ_r

Polar molecules

Molecules where one end is positive and one end is negative (causing a potential difference)

What do polar molecules do in an electric field?

Align themselves with the field

How will polar molecules interact with a capacitor’s electric field?

Oppose the field and increase capacitance

Electrical energy stored by a capacitor

Integral of a charge-P.D. graph

How does a capacitor charge?

Once current flows across a capacitor, negative charge builds up on the plate connected to the negative terminal and positive charge builds up on the plate connected to the positive terminal. The difference in potentials on each plate cause an electric field to be formed

Time constant

The time taken to discharge a capacitor to 1/e or charge to 1-1/e of its initial value

Magnetic flux density

A measure of the strength of a magnetic field

Tesla

Unit of magnetic flux density, equal to a force of 1N being exerted on 1m of a wire carrying 1A of current.

Fleming’s left hand rule for a wire in a field

For a current carrying wire in a magnetic field.

Thumb = Movement

Pointer = Field

Middle = Current (Positive to Negative)

Fleming’s left hand rule for a particle in a field

Thumb - Motion

Pointer - Field

Middle - Positive to negative flow (Reverse direction for a negative particle)

Which direction does the force on a charged particle in a field act relative to its motion?

Perpendicular/Circular motion

How does a cyclotron work?

Two hemispheric electrodes (dees) cause a magnetic field perpendicular to their planes. A high frequency AC voltage is applied. A centripetal force causes circular motion, and when the particles cross the gap between electrodes, they are accelerated. This causes them to travel with a wider radius, so eventually their speed is high enough to exit the cyclotron.

Magnetic flux

The number of magnetic field lines passing through a given area (ϕ = BA)

Magnetic flux linkage

The product of the magnetic flux and the number of turns in a coil

Electromagnetic induction

When an emf is produced due to a conductor experiencing a changing magnetic field

Faraday’s law

The magnitude of induced emf is equal to the rate of change of flux linkage (|ϵ| = |N dϕ/dt|)

Lenz’s law

The induced emf opposes the change in magnetic flux that produces it (ϵ = -N dϕ/dt)

Demonstrate Lenz’s law

A magnet falling through a coil will have a field induced when first entering that it equal to the falling pole (to repel), when leaving it will have an opposite field induced (to attract)

Formula for the emf induced in a constantly rotating coil in a field

Nϕ = BAN cos(ωt)

ϵ = - N dϕ/dt

ϵ = - BAN ω - sin(ωt)

ϵ = BAN ω sin(ωt)

What are the values for I_rms and V_rms

V/I_rms = V₀/I₀ / sqrt(2)

RMS voltage of the UK

230V

How does a transformer work?

A core of conductive material has two coils of wire on either side. The ratio of the turns one one side compared to the other is equal to the ratio of the voltage from one side compared to the other (N_s/N_p = V_s/V_p)

Step-up transformer

Increases voltage across the core

Step-down transformer

Reduces voltage across the core

Transformer efficiency

% = I_sV_s/I_pV_p

Eddy currents in a transformer

Energy losses that are induced by the alternating magnetic field in the primary coil. They form a loop within the core. They generate heat, causing energy to be lost

How to reduce eddy currents

Using a laminated iron core or by using a high-resistivity core

How to reduce general energy losses in transformers

Having low resistance coils, having thick wire or having a soft core (not easily magnetised)

How to reduce energy losses during transmission

Reducing current/Increasing voltage/Using a step-up transformer