# PHYS UNIT 4: ELECTRICFIELDS

• ELECTRICFIELDS
• CAPACITORS
• MAGNETIC FIELDS AND FORCES
• CHARGED PARTICLES IN MAGNETIC FIELDS
• ELECTROMAGNETIC INDUCTION
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• Created by: Chynna
• Created on: 12-04-13 16:42

## ELECTRICFIELDS

There is an electric field around a charged object

• region where it can attract/repel other charges
• Charge measured in coulombs (C)
•  If charged object is placed in an electric field, it will feel a force

Can calculate force using coulomb’s law

•  = permittivity of material between charges
•  -r is the distance between Q1 and Q2
•  If the charges are opposite, force is attractive, F will be negative
• If the charges are alike, force is repulsive, F will be positive
•  Force of Q1 is always equal and opposite to the force on Q2
•  It’s an inverse square law – the further apart the charges are, the weaker the force between them
• The size of force also depends on the permittivity of the material between the 2 charges, for free space it is: 8.85 x 10-12 C2N-1m-2
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## ELECTRICFIELDS

Electric fields can be radial or uniform

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## ELECTRICFIELDS

Electric field strength is force per unit charge

•  E – force per unit positive charge, the force that a charge of +1C would experience if it was placed in an electric field
•  E is a vector pointing in the direction that a positive charge would move
• Units = newtons per coulomb
•  Field strength is like the measure of how tightly packed the field lines are
• In a radial field, the field strength depends on how far you are from the charge
• In a uniform field, the field strength is the same everywhere

In a radial field, E is inversely proportional to r2

·         As you go further away from a point charge Q, the field lines get further apart and the field strength decreases

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## ELECTRICFIELDS

In a uniform field, E is the same everywhere

• Field lines are parallel – field strength is the same at all points within the field
• Field strength between 2 parallel plates depends on the potential difference, V, and the distance, d, between them
•  E = V/d

Investigating a uniform field

• An atomiser creates a fine mist of oil drops that are charged by friction as they leave the atomiser
• When the circuit is off, the drops fall from the plate to the bottom plate due to their weight
• When it is switched on, the p.d. between the plates creates a uniform electric field, which exerts a force on the oil drops. A negatively charged oil drop can be made to ‘float’ between the plates by balancing the upward force from the electric field w/ the
•  If you increase the p.d., you increase the field strength so the oil drop moves towards the positive top plate
• If you increase the distance between the plates or decrease the p.d., you reduce the field strength + the oil drop falls from the bottom plate due to its weight
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## CAPACITORS

Capacitance – amount of charge stored per volt

C = Q/V – units = farads (F)

Investigate the charge stored by a capacitor experimentally

• Set up a test circuit 6to measure current and pd
• Constantly adjust the variable resistor to keep the charging current constant for as long as you can
• Record the pd at regular intervals until it equals the battery pd
• From these results you can plot the following graphs: current against time and charge against pd

Capacitors store energy

• When switch is flicked to the left, charge builds up on the plates of the capacitor. Electrical energy, provided by the battery, is stored by the capacitor
• If switch is flicked to right, energy stored on the plates will discharge through the bulb, converting electrical energy into light and heat
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## CAPACITORS

• Work is done removing charge from 1 plate and depositing opposite charge onto the other one. Energy for this must come from the electrical energy of the battery, given by charge x pd. Energy stored by the capacitor = work done by battery
• You can find the energy stored by the capacitor from the area under a graph of pd against charge stored on the capacitor. Pd across a capacitor is proportional to the charge stored on it, graph will be a straight line through the origin.
•  Area of triangle = ½ x base x height, W = 1/2QV W = work done BUT it can also be E

3 expressions for the energy stored by a capacitor

W = 1/2QV

W = 1/2CV2

W = Q2/2C

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## CHARGING AND DISCHARGING

You can charge a capacitor by connecting it to a battery

• When capacitor is connected to a battery, a current flows in the circuit until capacitor is fully charged, then stops
• The electrons flow onto the plate connected to the negative terminal so a negative charge builds up
• The build up of negative charge repels electrons off the plate connected to the positive terminal of the battery, making that plate positive. These electrons are attracted to the positive terminal of the battery
• An equal but opposite charge builds up on each plate, causing a pd between the plates. remember that no charge can flow between the plates because they’re separated by an insulator (dielectric)
• Initially the current through the circuit is high. But as charge builds up on the plates, electrostatic repulsion makes it harder and harder for more electrons to be deposited. When the pd across the capacitor is equal to the pd across the battery, the current falls to 0. The capacitor is fully charged
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## CHARGING AND DISCHARGING

To discharge a capacitor, take out the battery and reconnect the circuit

• When a charged capacitor is connected across a resistor, the pd drives a current through the circuit
• Current flows in the opposite direction from the charging current
• The capacitor is fully discharged when the pd across the plates and the current in the circuit are both 0.

The time taken to charge or discharge depends on 2 factors

• The capacitance of the capacitor (C) – affects the amount of charge that can be transferred at a given voltage
• Resistance of the circuit (R) – affects the current on the circuit

Charge on a capacitor decreases exponentially

• Always takes the same length of time for the charge to halve, no matter how much charge start with
• Charge left on the plates of a capacitor discharging from full – Q = Q0
• The graphs of V against t and I against t for charging and discharging are also exponential
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## CHARGING AND DISCHARGING

Time constant   = RC

• Time constant = time taken for the charge on discharging capacitor to fall to 37% of Q0
• Also the time taken for the charge of a charging capacitor to rise to 63% of Q0
• The larger the resistance in series w/ the capacitor, the longer it takes to charge/discharge
• In practise, the time taken for a capacitor to charge/discharge fully is taken to be about 5RC
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## MAGNETIC FIELDS AND FORCES

Magnetic field – region where a magnetic force is exerted on magnetic material

• Can be represented by field lines, go from north to south
•  The closer the lines are together, the stronger the field

There a magnetic field around a wire carrying electric current

• Direction of a magnetic field can be worked out w/ the right hand rule

Magnetic flux is like the total no. of field lines

• Magnetic field strength / magnetic flux density, B – measure of the strength of the magnetic field per unit area. Vector quantity, measured in teslas, T
• Magnetic flux   = BA (B = magnetic field) for the total magnetic flux passing through an area perpendicular to B
• When you move a coil in a magnetic field, the size of the emf induced depends on the magnetic flux and the no. of turns on the coil. Product of these = flux linkage
• Flux linkage    = N    = BAN
• Units of both magnetic flux and flux linkage = weber, Wb – a change in flux of 1 weber per second will induce an electromotive force of 1 volt in a loop of wire
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## MAGNETIC FIELDS AND FORCES

A wire carrying a current in a magnetic field will experience a force

• A force acts if a current-carrying wire cuts magnetic flux lines
• If the current is parallel to the flux lines, no force acts
• The direction of the force is always perpendicular to both the current direction and the magnetic field
• Direction of force is given by fleming’s left-hand rule

Size of force can be calculated

• Size of force, F, on a current-carrying wire at right angles to a magnetic field is proportional to the current, I, the length of wire in the field, l, and the strength of the magnetic field, B. F=BIl
• Magnetic field strength, B – force on 1m of wire carrying a current of 1amp at right angles to the magnetic field

The force is greatest when the wire and field are perpendicular

• Force is caused by the component of field strength which is perpendicular to the wire, Bsin
• So, for a wire at an angle   to the field, the force acting on the wire is given by: F = BIlsin
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## CHARGED PARTICLES IN MAGNETIC FIELDS

Forces act on charged particles in magnetic fields

•  Electric current in a wire is caused by the flow of negatively charged electrons – which are affected by magnetic fields.
• Force exerted on a current-carrying wire in magnetic field perpendicular to the current = BIl
• Force acting on a single charged particle moving perpendicular to a magnetic field = Bqv or B=Bqvsin

Charged particles in a magnetic field are deflected in a circular path

• By fleming’s left hand rule the force on a moving charge in a magnetic field is always perpendicular to its direction of travel
• This is the condition for circular motion
• This effect is used in particle accelerators
• Radius of curvature of the path of a charged particle moving through a magnetic field gives you info. about the particle’s charge and mass – you can identify diff particles by studying how they’re deflected
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## CHARGED PARTICLES IN MAGNETIC FIELDS

Charges accumulate on a conductor moving through a magnetic field

•  If a conducting rod moves through a magnetic field, its electrons will experience a force – they will accumulate at one end of the rod
• This induces an emf across the ends of the rod exactly as a battery would
• If the rod part of a complete circuit, then an induced current will flow through it – electromagnetic induction
• An emf is induced whenever there is relative motion between a conductor and magnet
• The conductor can move and the magnetic field stay still or the other way round
• An emf is produced whenever lines of force (flux) are cut
• Flux cutting always induces emf but will only induce a current if the circuit is complete

Emf is proportional to rate of change of flux linkage

• Faraday’s law: the induced emf is directly proportional to the rate of change of flux linkage
• Induced emf = flux change / time taken = dBAN / dt
• Size of the emf is shown by the gradient of a graph of flux linkage against time
• The area under the graph of emf against time = flux linkage
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## ELECTROMAGNETIC INDUCTION

The direction of the induced emf and current are given by Lenz’s law

• Lenz’s law: the induced emf is always in such a direction as to oppose the change creating it
• Lenz’s law and faraday’s law can be combined to give = induced emf = -d(BAN) / dt
• Minus sign = direction of the induced emf
• The idea that a induced emf will oppose the change that caused it agrees with the principle of the conservation of energy – energy used to pull a conductor through a magnetic field, against the resistance caused by magnetic attraction, is what produces the induced current
• Lenz’s law can be used to find the direction of an induced emf and current in a conductor travelling at right angles to a magnetic field...
• -Lenz’s law states that the induced emf will produce a force that opposes the motion of the conductor – a resistance
• -Using fleming’s left hand rule, point your thumb in the direction of the force of resistance – which is in the opposite direction to the motion of the conductor
• Your second finger will now give you the direction of the induced emf
• If the conductor is connected as part of a circuit, a current will be induced in the same direction as the induced emf
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## ELECTROMAGNETIC INDUCTION

You can change the amount of emf induced in a coil by changing one of the factors:

• The angle between the coil and the field – the more aligned the coil is to the field, the fewer the field lines it will cut through, so the smaller the emf induced
• Number of turns of the coil – higher the no. of turns, the more points in the coil will cut each flux line, the higher the emf induced in the coil
• Area of the coil – larger the area, more flux lines will pass through it and so the higher the emf induced
• Magnetic field strength (flux density) – higher the flux density, the more flux lines there will be per unit area, so the coil will cut more flux, inducing a greater emf
• Angular speed of the coil – increasing the rate the coil rotates at increases the no. of flux lines cut by the coil in a given time – increases voltage induced in coil

An alternator is a generator of alternating current

• Generators or dynamos – convert kinetic energy into electrical energy – they induce an electric current by rotating a coil in a magnetic field
• Output voltage and current change direction with every half rotation of the coil, producing alternating current (AC)
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## ELECTROMAGNETIC INDUCTION

Transformers work by electromagnetic induction

• Change the size of the voltage for an alternating current – use the same principle of flux linking 2 coils of wire
• An alternating current flowing in the primary (or input) coil produces magnetic flux
• The magnetic field is passed through the iron core to the secondary (or output) coil, where it induces an alternating voltage of the same frequency
• Step up transformers increase the voltage by having more turns on the secondary coil than the primary and step down transformers have it the opposite way round.
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