SACE Stage 2 - Physics Topic 2: Electricity & Magnetism

What is an electric field?

An electric field is a region of space where a charged object experiences an electric force.

• Produced by charged objects.

• Represented by electric field lines.

• Direction is the direction a positive test charge would move.

How do electric field lines behave?

• Start on positive charges.

• End on negative charges.

• Never cross.

• Closer lines indicate stronger fields.

• Point in the direction of force on a positive charge.

Field line density = field strength.

Explain why electric forces are consistent with Newton's Third Law.

The force exerted by q1 onto q2 is equal is magnitude but opposite in direction to the force exerted by q2 onto q1.

F_AB = - F_BA

Why does the electric field near sharp points ionise air?

At sharp points:

• Electric field lines become highly concentrated.

• Field strength becomes very large.

The strong field:

1. Accelerates electrons in nearby air molecules.

2. Electrons collide with other molecules.

3. Additional electrons are knocked free.

Ionisation of air particles due to sharp points

• Air becomes conductive.

• Charge can leak away.

• Results in corona discharge.

Describe the motion of a charged particle parallel to a uniform electric field.

If the particle moves parallel to the field:

• Force acts in the direction of motion.

• Particle accelerates.

• Velocity increases.

Positive charge:

• Accelerates in field direction

Negative charge:

• Accelerates opposite field direction

Describe the motion of a charged particle antiparallel to a uniform electric field.

If moving opposite the force:

• Particle slows down

• Kinetic energy decreases

• May stop and reverse direction

How does an electric field transfer energy to an ion between cyclotron dees?

Between the electrodes:

• There is a potential difference

• An electric field exists.

As the ion crosses:

• Electric force performs work

• This work becomes kinetic energy

• Thus increasing speed and kinetic energy

How can ions be accelerated to very high energies?

• The ion repeatedly crosses the gap between the electrodes

• Adds more kinetic energy

• More kinetic energy is gained every crossing

• Speed increases continuously

After many crossings:

• very high levels of kinetic energy

Why do ions not gain kinetic energy inside the electrodes?

Inside the electrodes:

• Electrodes are absent of an electric field since they are hollow conductors (provided there is no electric field inside the cavity)

• this is because of the free movement of the ‘sea’ of electrons within the walls of the hollow conductor

• Thus no work is done, speed and kinetic energy remain constant

Describe the magnetic field around a straight current-carrying conductor.

Field Lines:

• concentric circles around wire

• strongest near wire

• weaker further away

Describe the magnetic field around a current loop.

• one side acts as a North pole

• other side acts as a South pole

• Field strongest through centre

Describe the magnetic field of a solenoid.

Inside:

• Nearly uniform magnetic field

• Strong field lines

• Parallel field lines

Outside:

• functions as magnetic dipole with two distinct poles that produce an external field that loops from the one end to the other.

 What determines the magnetic force on a moving charged particle?

The magnitude of the magnetic force on a moving charge is proportional to the particle's charge, speed, and the field strength, reaching a maximum when moving perpendicular to the field and zero when moving parallel to it.

Why does a charged particle move in a circle when entering a magnetic field at right angles?

• A charged particle entering a magnetic field at right angles moves in a circle because the magnetic force acts mutually perpendicular to its velocity.

• This force functions purely as a centripetal force, continuously altering the particle's direction while keeping its speed constant, which creates a circular path with a fixed radius

What magnetic field is required inside a cyclotron?

• magnetic field must be strong and uniform and positioned perpendicular to the electrodes

• this ensures the frequency of the particle’s revolution remains constant and independent of its speed

• by holding the frequency constant, the alternating electric field can continuously accelerate the ions

How does the magnetic field keep ions moving in circles?

• keeps ions moving in circles since magnetic force is perpendicular to velocity of charged particle

• the magnetic force acts as a centripetal force by directing the particle radially inwards

• this continuously changes the direction of the particle’s velocity but keeps speed constant

• this forces the particle into a circular trajectory of a fixed radius

• the magnetic field only changes direction, speed is constant

Why does a magnetic field not increase kinetic energy?

• because magnetic force is always perpendicular to velocity

• since the magnetic force is at a right angle to the direction of motion, it performs zero work on the particle

• thus the particle’s kinetic energy and speed remain completely constant, changing only its direction as W=change in E_k and the kinetic energy is unchanged.

State Faraday's Law.

states that the magnitude of the induced emf in a conducting circuit is directly proportional to the time rate of change of the magnetic flux threading through the circuit.

State Lenz’s Law.

states that the direction of an induced electromotive force and subsequent induced current will always be such that it creates a magnetic field that opposes the original change in magnetic flux that caused it

How does conservation of energy explain Lenz's Law?

• a magnetic field with alternating polarities induces an emf

• the emf produces a current

• the magnetic field of the current opposes the change in magnetic flux

• this ensures the original flux is maintained through the system when the current flows through it

• this is because energy can only be transferred or transformed.

How do you determine induced current direction using Lenz's Law?

Step 1:
Determine whether magnetic flux is increasing or decreasing.

Step 2:
Determine the field needed to oppose that change.

Step 3:
Use right-hand grip rule to find current direction.

What are eddy currents?

loops of electrical current induced within a bulk piece of solid conductor when it experiences a changing magnetic flux, flowing in paths that oppose the original change in flux.

Characteristics:

• Cause heating.

• Waste energy.

• Create opposing magnetic fields.

How are eddy currents reduced?

by using laminated structures or slotted designs in solid conductors, which introduce high-resistance pathways that disrupt and minimise the size of the circulating current loops

Thin insulated layers:

• Break current loops.

• Reduce current magnitude.

• Reduce heating losses.

How does a generator produce electricity?

An electric generator produces electricity by converting mechanical energy into electrical energy through electromagnetic induction, where a coil rotating inside a magnetic field experiences a continuously changing magnetic flux

• mechanical energy —> electrical energy

Why is alternating current produced by generators?

• the rotating coils continuously reverses its orientation relative to the magnetic field

• this causes the rate of change of magnetic flux to change direction every half-turn

What is the purpose of a transformer?

• changes the voltage and current of an alternating current electricity supply

• does this while still keeping the frequency and electrical power constant

• used to improve efficiency of power transmission

How does a transformer work?

• by using mutual emf induction to transfer electrical energy between two electrically isolated coils

• the coils are wound around a shared magnetic core

• this converts the voltage and current of an alternating current supply

What is corona discharge?

• a localised electrical discharge

• occurs when a high accumulation of charge at a sharp point creates an electric field

• this electric field is strong enough to steal electrons from surrounding air molecules

• the ionised air molecules then cause a chain of continuous ionisation reactions to other nearby particles.

• this makes the air conductive