MAGNETIC FIELDS TO REMEMBER (finish)

Magnetic field

The force field around a magnetic object is a magnetic field. A force field is a region where a body will experience a non contact force.

Magnetic field line

The direction, and relative magnitude, of force on an isolated North pole placed in a magnetic field

Magnetic field strength / flux density, B

Force per unit length per unit current on a current-carrying conductor perpendicular to the magnetic field lines

The Tesla

The strength of the magnetic field that

producesaforceof1Ninawireoflength1mwith 1 Ampere flowing perpendicular to the field

Motor effect

When a current carrying wire placed at a non-zero angle to the field lines of an external magnetic field experiences a force due to the field.

Fleming's Left Hand rule

Used to determine the direction of the force on the wire relative to the direction of the field and the direction of the current.

Electromagnetic induction / generator effect

When a wire cuts across the lines of a magnetic field, an e.m.f. Is induced. If the wire is connected in a circuit, a current is induced

Fleming's Right Hand rule

Used to determine the direction of the induced current relative to the direction of the field and the direction of the motion of the wire

Lenz's Law

The direction of the induced emf when there is a change of flux linkage is such that it will try to oppose the change of flux that is producing it

Magnetic flux, Φ

The product of the magnetic flux density, B, and the area swept out. A. Can be thought of as the net number of field lines passing through - and perpendicular to - the area

Magnetic flux linkage

Magnetic flux linkage through a coil of N turns is the product of N and the magnetic flux through each turn. Can be thought of as an extension to the idea of magnetic flux for a coil

- DO NOT CANCEL OUT THE N's

Faraday's Law of Induction

The induced emf in a circuit is equal to the rate of change of flux linkage through the circuit

- relates the rate of change of flux linkage to the e.m.f. Induced in a conductor

Back e.m.f

An e.m.f. induced in the spinning coil of an electric motor because the flux linkage through the coil changes

R.M.S. current / voltage

The root-mean-square value of an alternating current is the value of direct current that would give the same heating effect as the alternating current in the same resistor. The R.M.S. of an alternating current or p.d.

How does a transformer work - 5 steps

1. The alternating voltage in the primary coil induces an alternating current in the primary coil

2. The alternative current creates an alternating magnetic flux

3. The soft iron core serves to direct the flux produced around the primary coil since it is easily magnetised and demagnetised (provides greater flux linkage from p to s coil compared to an air core)

4. The alternating flux is directed through the iron core to the secondary coil inducing an alternating emf in the secondary coil

5. This is because an egg is induced when there is a rate of change of flux linkage

Why cab we only use an AC voltage source in transformers and not DC

- the AC voltage in the primary coil produces an alternating current and a varying magnetic flux

- the varying magnetic flux when links to the secondary coil induces an EMF

- EMF is only induces when there is a change in flux

- A DC voltage produces a steady current and an unchanging flux so no emf is produced

For a given input voltage, what does the output voltage produced in the secondary coil depend on

- the output voltage produced in the secondary coil depends on the number of turns

- a higher number of turns in the secondary coil induces a voltage greater than the input voltage

- a lower number of turns in the secondary coil induces a voltage lower than the input voltage

Step up transformer

Has more turns on the secondary coil than on the primary coil, so increases the voltage

Step down transformer

Has fewer turns on the secondary coil than on the primary coil, so decreases the voltage.

Transformer inefficiencies - 4

1. energy is needed to magnetise and demagnetise the core and this energy is wasted as it heats up the core

2. in practice, not all the flux created in the primary coil cuts through the secondary coil (particularly if the coils are far apart)

3. heat is generated by the resistance in the coils

4. the magnetic flux created in the primary coil cuts through the metal core, inducing an emf in the core - causes an Eddy current to flow causing the core to heat up and energy to be lost

Problem: 'energy is needed to magnetise and demagnetise the core and this energy is wasted as it heats up the core'

Use a magnetically soft material like a soft iron which magnetises and demagnetises easily

- soft means less work needs to be done to magnetise it

∴ less energy is lost

Problem: 'in practice, not all the flux created in the primary coil cuts through the secondary coil (particularly if the coils are far apart)'

To reduce magnetic loss & to direct all the flux from primary to secondary coil, the core is designed so that the coils are closer together

Problem: 'heat is generated by the resistance in the coils'

Use low resistance wires

- thick & low resistivity

- thick copper wires are usually used as it has a larger diameter & a lower resistivity

- a shorter wire is also helpful but difficult as a minimum number of coils are needed

Problem: 'the magnetic flux created in the primary coil cuts through the metal core, inducing an emf in the core - causes an Eddy current to flow causing the core to heat up and energy to be lost'

Laminate the core (layers of core separated out by thin layers of insulator)

Eddy currents

Small closed loops of electric current induced within conductors by a changing magnetic field in the conductor or by the relative motion of a conductor in a magnetic field

How do Eddy currents arise + how does it slow down a device

- a current in the electromagnet induces a magnetic field in the electromagnet (SOMETIMES RELEVANT)

- as something move through the magnetic field it causes a change in magnetic flux (Faradays)

- this forms an EMF & an Eddy current

- the Eddy current opposes the motion of the rotating object by producing an opposing force (lenz)

- this slows down the object

How to reduce the effect of Eddy currents

make transformer cores out of laminated iron rather than solid iron

- introduce slots by introducing air (an insulator) in between

- slots with an insulator have a higher overall resistance ∴ smaller Eddy current ∴ less heat loss

- smaller area for the current so tinier Eddy currents are produced ∴ less heat loss

Direction of Force on a Moving Charge in a uniform magnetic field

+ive Q = current points in the same direction as its velocity

-ive Q = current points in the opposite direction to its velocity

Direction of Force on a Moving Charge in a radial magnetic field

(into the page)

+ive Q = same direction as current, anticlockwise

-ive Q = opposite direction as current, clockwise

Direction of Force on a Moving Charge in a radial magnetic field

(out the page)

+ive Q = same direction as current, clockwise

-ive Q = opposite direction as current, anticlockwise

How is r=mv/BQ formed & what does it show

Faster moving particles with speed v move in larger circles (larger r):

Particles with greater mass m move in larger circles:

Particles with greater charge q move in smaller circles:

Particles moving in a strong magnetic field B move in smaller circles:

Two situations in which a charged particle will not experience a magnetic force when placed in a magnetic field

1) not moving - no velocity

2) moving parallel to the force

What is a cyclotron

A type of particle accelerator which makes use of the circular trajectory of charged particles in a magnetic field to create a spiral path and accelerates charged particles, such as protons, to very high speeds

Applications of a cyclotron

- to produce tracers for imaging

- to create high-energy beams of radiation for radiotherapy

How does a cyclotron work

Role of the uniform magnetic field in a cyclotron

To supply the centripetal force needed to keep the particles moving in a circular motion

- as a charged particle travels around a single Dee they follow a circular path of constant radius at constant speed

Role of the electric friend in a cyclotron

To accelerate the particles between the dees

- as the charged particles travel across the gap between dees they gain additional energy and move faster + follow a path with a larger radius as the enter the next Dee

What is the change in kinetic energy associated with each half-circle in a dee

There's no change inside a dee as no work is done

Mass spectrometer

An instrument that can be used to measure the masses of isotopes

2 experimental phenomena

1. Moving a magnet through a coil

2. Moving a wire through a magnetic field

Experimental phenomena - moving a magnet through a coil

Experimental phenomena - moving a wire through a magnetic field

Straight conductor moving in a magnetic field

EMF induced in a coil rotating uniformly in a magnetic field

- coil rotates in a uniform magnetic field, the flux through the coil varies

- EMF = the rate of change of flux linkage so emf will also change as the coil rotates

- The maximum EMF is when the coil cuts through the most field lines

- Induced by an alternating voltage

Flux linkage against time

COS graph

when the plane of the coil is perpendicular to the field lines → maximum

when the plane of the coil is parallel to the field lines → zero

EMF against time

when the plane of the coil is perpendicular to the field lines → zero

when the plane of the coil is parallel to the field lines → maximum

USE OF AN OSCILLOSCOPE AS A DC AND AC VOLTMETER, TO MEASURE TIME INTEVALS AND FREQUENCIES AND TO DISPLAY AC WAVEFORMS