**Fields**

Force field- a region in which body experiences a non-constant force.

A field is a physical quantity that describe a conduction in the space. The conduction or value could be scalar or vector.

For each point in space, field is described by

- field strength – force per unit (mass / Charge) – vector
- Field potential – energy per unit ( mass / charge) – scalar

Gravitational force

- are caused by mass
- mass attract other mass (gravitational field are always attractive).
- the effect of the field is infinite.

Drawing of Field

- Field strength is represented by “field lines” “line intensity” (how close the lines are) gives relative value to field strength.
- the direction of the force is given by the arrows.

Example: Earth’s gravitational field

2 equal masses interacting

All gravitational fields are radial.

However due to the relative size in certain situation, it is better modeled as uniform field.

Newton’s universal law of gravitation.

- For two point like masses (no volume)

From this we know:

gravitational field strength

Gravitational potential

Gravitational potential – is the work done in moving a mass from point of separation of infinity (r = ∞) to the point in the field in question.

Electric Fields

An electric field is a region in which particles experiences a force.

electric fields are due to charge (+ve , -ve)

Drawing electric fields

field line show relative strength and direction that positive charge would ‘fee’ a force.

Electric field strength (E) at a point in a field is defined as force per unit charge on a positive test charge placed at that point.

Electric field strength in uniform field

Electric potential – at a certain position in any electric field is defines as the work done per unit charge on positive test charge when it is moved from infinity to that position.

Coulomb’s Law

states that the force between two charged particle is proportional to the product of their charges and inversely proportional the square of their separation.

Capacitance

Capacitance – the charge per unit volt,

A capacitor is device that store electric charge.

a capacitor consists of two conductor separated bu insulator.

Dielectrics

a dielectric is a insulating material by paper, plastic, glass.

a dielectric placed between the conductor of the capacitor increases its capacity by factor k called the dielectric constant.

different insulator have different permitivity ε**.**

for example: glass k =5 . therefore ε_{glass }is 5 * ε_{ air}.

Increasing capacitance:

Inserting a dielectric

the charges plates cause the dielectric to polarize and align. This cause an induced charge on each side of the dielectric.

E_{1} = electric field caused by charged particles

E2= smaller electric field caused bu opposing ends of dielectric.

Not elecric field = E_{1} – E_{2}

therefore inserting the dielectric cause the net electric field to decrease.

Adding a dielectric to a charging capacitor

- Dielectric become polarized
- capacitance increases C= ε A/d
- voltage still remain constant so due to C = Q/V , Q must increase.
- this is because the polarized molecule in dielectric negate so,e of the surface charge, allowing more charge on to the capacitor plates.

Adding a dielectric to a charged capacitor

- dielectric become polarized
- Capcitance increases ( C= ε A/d)
- as capacitor is disconected , there is nowhere for the charge to move, so due to C= Q/V, the voltage across the plates must decrease.
- from electric field, we know , a uniform electric field is calculated from E = V/d so E ∝ V.

the electric field has decreased. As E ∝ V the voltage therefore decreases across the plates and therefore there is an increase in the capacitance.

Charging a capacitor

- the rate of charge of voltage decreases.
- as the potential difference across the plate increases, more charge fill the plates and it gets harder to add more charge due to the repelling force. The current shows the p.d across the plates gets closer to the equaling pd of the battery.
- pd is promotional to the charge so, their graph looks the same.

- current shows the rate of change of charge (dQ/dT).
- Current flows fast to the start with but slows down as a capacitor becomes more charged.

Discharging a capacitor

- Initially there is a large current due to the large potential difference across the plates. as the potential difference drops so, does the current, as there is less electric force pushing the electrons around the circuit.

Note :

the current is negative compared to the charging as the electrons flow in opposite direction.

- the charge drops quickly at first (due to the large current, the flow of charge away from the capacitor).
- As pd and charge are propotional, they look the same.

Discharge the capacitor by connecting two plates by using a conductor.

Time Constant

Capacitor discharge “exponentially”.

The rate of removal of charge is proportional to the amount of charge remaining.

after each time constant T, the cahrge drops by the same proportion each time.

Time constant (T) = Resistance (Ω) * Capacitance (F)

Time contant – the time taken to reach 37% of original charge when discharging.

where Q_{o}, V_{o} and I_{o} are the max. charge,Voltage and Current.

RC is the time constant.

t is the time

Capacitor in series

In series, capacitor have same amount of charge stored on them because charge from the first one travels to the rest.

The voltage is the spread out among the capacitors.

Capacitor in parallel

Two small capacitor in the parallel can be thought of as being same one big capacitor.

therefore adding capacitor in parallel will increase the space available to store charge and will increase the capacitance.

**Magnetic Field**

Magnetic Field- a region in which a particle with magnetic properties experiences a force and in which a moving charge experiences a force.

magnetic flux density (B0 – the strength of the magnetic field. Tesla (T)

Magnetic field patterens

Two parallel bar magnets

Magnetic field due to the current charging wire

- passing a current through a wire creates a magnetic field around the wire.
- If present, this magnetic field will interact with another external magnetic field.
- The 2 field interaction produces a force.
- the force could be used to create the motion — motion effect

The force on a current carrying wire in magnetic filed

A current carrying wire placed at a non-zero angle to a B field experiences a force.

This force is:

- greater when the wire is at right angle to the B field.
- zero when the wire is parallel to the magnetic field.

Flemming’s left hand rule

when flemming came up with the left hand rule, they (scientist) believed that current was the flow of positive particles. This is known as “conventional current”.

If a question uses

- A positive charge, point I in the direction of the positive charges velocity.
- A negative charge, point I in the opposite direction to its velocity.
- “first current” with no charge goes, just use the left hand rule as usual.

Moving Charges within fields

Scene A – Gravitational field

- ball throen horizontally on the surface of earth.

Scene B – Electric Field

- moving charges in the uniform electric field.

- in field path is parabolic
- outside field continues a linear path.

Scenerio C – Magnetic field

- charged particles in uniform B-field

- Force acts on particle when inside B-Field.
- Force always acts perpendicular to the velocity creating a circular path.

Force on a moving Charge

in a magnetic field F = BQV acts as the Centripetal force to cause circular motion. Thereforeyou can equate F= BQV with F= mv^{2}/r to create

and you can rearrange for r.

What we have seen

- we can create a force (motion) from a B-Field and a current carrying wire.

however opposite can also occur, we can induce emf using a B-fied.

A = cross sectional area of the coil (m^{2}) N= number of coil turns (unit-less)

Faraday’s law of EM induction:

“The induced emf in the circuit is equal to the rate of charge of the flux linkage to the circuit.”

When you move a conductor through a B-field. a force acts on the delocalized electrons inside the conductor. this causes the electrons to move, creating a potential difference (emf). if a circuit is made, a current can flow.

The alternating Current generator

- As the coil spins at the steady rate, there is a continuous charge in flux linkage.

Alternating Current and the Power

peak value = maximum value

r.m.s = root mean square — used to create a non zero charge.

Transformers

transformer- a device that can alter the input voltage (and consequently the current).

if the transformer is 100% efficient

power in= power out

in this case and P =IV , if V increases, I will decrease and vice versa.

How it works

- The alternating current passing through the primary coil creates a B-Field.
- The fact it is alternating means it creates a continuous alternating B-Field.
- This in turn creates a continuous charging magnetic flux and therefore emf.
- If a direct current was used, a B-Field would still be created, However it will not b charging and therefore blip of emf would be seen but then nothing.

Currently this transformer is not very efficient as a lot of the magnetic field is lost.

To fix this, we put in a core, this is the material that can easily be magnetized and allows the B-filed to flow through it.

Soft iron-

- easily magnetized and demagnetized, so doesn’t heat up as much — less energy lost

Laminated core –

- smaller region for electrons to move in.
- smaller eddy currents.
- less back emf and therefore less heating.

Thick low resistivity winding – P + I^{2}R – low resistance so, less heat loss.