Book Reference : Pages 113-115Book Reference : Pages 113-115

1.1. To understand that the path of a charged To understand that the path of a charged particle in a magnetic field is circularparticle in a magnetic field is circular

2.2. To equate the force due to the magnetic field To equate the force due to the magnetic field to the centripetal forceto the centripetal force

3.3. To examine practical applications of circular To examine practical applications of circular particle displacementparticle displacement

In the previous lesson we have seen that a moving In the previous lesson we have seen that a moving charged particle is deflected in a magnetic field in charged particle is deflected in a magnetic field in accordance with Fleming’s left hand ruleaccordance with Fleming’s left hand rule

Electron Gun

Magnetic field coming out of the page

Initial Path of the Electron

Force

ConventionalCurrent

Electron Gun

Force

ConventionalCurrent

Electron Gun

Force

The force acts perpendicular to the velocity causing the path to The force acts perpendicular to the velocity causing the path to change.... The force acts perpendicular to the velocity causing the change.... The force acts perpendicular to the velocity causing the path to change.... The force acts perpendicular to the velocity path to change.... The force acts perpendicular to the velocity causing the path to change.... causing the path to change.... Circular motion is achievedCircular motion is achieved

ConventionalCurrent

The force on the moving charged particle is always at The force on the moving charged particle is always at right angles to the current velocity... Circular motion!right angles to the current velocity... Circular motion!

As always with circular motion problems we are looking As always with circular motion problems we are looking a the force to “a the force to “equateequate” to the centripetal force” to the centripetal force

From the last lesson we saw that the force on a charged From the last lesson we saw that the force on a charged particle is F= BQvparticle is F= BQv

BQv = mvBQv = mv22 / r / r

r = mv/BQr = mv/BQ

The path becomes The path becomes moremore curved (r reduced) if the flux curved (r reduced) if the flux density increases, the velocity is decreased or if particles density increases, the velocity is decreased or if particles with a larger specific charge (Q/m) are usedwith a larger specific charge (Q/m) are used

VelocityBQv

A beam of electrons with a velocity of 3.2x10A beam of electrons with a velocity of 3.2x1077 m/s is fired into a uniform magnetic field which m/s is fired into a uniform magnetic field which has a flux density of 8.5mT. The initial velocity is has a flux density of 8.5mT. The initial velocity is perpendicular to the field. perpendicular to the field.

Explain why the electrons move in a circular Explain why the electrons move in a circular orbitorbit

Calculate the radius of the orbitCalculate the radius of the orbit

What must the flux density be adjusted to if the What must the flux density be adjusted to if the radius of the orbit is desired to be 65mmradius of the orbit is desired to be 65mm

[21mm, 2.8mT][21mm, 2.8mT]

The magic A2 crib sheet quotes the following :The magic A2 crib sheet quotes the following :

Charge on an electron (e) = -1.6 x 10Charge on an electron (e) = -1.6 x 10-19-19 C CElectron rest mass (mElectron rest mass (mee)= 9.11 x 10)= 9.11 x 10-31-31 kg kg

However it also quotes...However it also quotes...

Electron Charge/Mass ratio(e/mElectron Charge/Mass ratio(e/mee) = 1.76x10) = 1.76x101111 C/kg C/kg

Two things.... Do not be phased by this since they could Two things.... Do not be phased by this since they could quote this for another particle... Simply inverting it (m/Q) quote this for another particle... Simply inverting it (m/Q) for this sort of calculation saves one step in the calculator!for this sort of calculation saves one step in the calculator!

Last lesson we saw the CRT (Cathode Ray Tube)Last lesson we saw the CRT (Cathode Ray Tube)

Such devices can also Such devices can also be calledbe called

Electron gunsElectron gunsThermionic devicesThermionic devices

The cathode is a heated filament with a negative potential The cathode is a heated filament with a negative potential which emits electrons, a nearby positive anode attracts which emits electrons, a nearby positive anode attracts these electrons which pass through a hole in the anode to these electrons which pass through a hole in the anode to form a beam. This is called form a beam. This is called Thermionic emissionThermionic emission. The . The potential difference between the anode and cathode potential difference between the anode and cathode controls the speed of the electrons.controls the speed of the electrons.

These are machines which can These are machines which can be used to analyse the types of be used to analyse the types of atoms, (and isotopes) present atoms, (and isotopes) present in a samplein a sample

r = mv/BQr = mv/BQ

The key to how it works is the The key to how it works is the effect that the mass has on the effect that the mass has on the radius of the circular motion while radius of the circular motion while keeping the velocity and flux keeping the velocity and flux density constantdensity constant

First we need to ionise First we need to ionise the atoms in the the atoms in the sample so that they sample so that they become charged... become charged... Electrons are removed Electrons are removed yielding a positive ionyielding a positive ion

A component known as a “A component known as a “velocity selevelocity selector” is key ctor” is key to obtaining a constant velocityto obtaining a constant velocity

The +ve ions are acted upon The +ve ions are acted upon by both an electric field & a by both an electric field & a magnetic field. magnetic field.

Only when they are equal & Only when they are equal & opposite do the ions pass opposite do the ions pass through the slitthrough the slit

Collimator withslit

Cyclotrons are a method of producing high energy beams Cyclotrons are a method of producing high energy beams used for nuclear physics & radiation therapyused for nuclear physics & radiation therapy

An alternating electric field is An alternating electric field is used to accelerate the used to accelerate the particles while a magnetic particles while a magnetic field causes the particles to field causes the particles to move in a circle, (actually a move in a circle, (actually a spiral since the velocity is spiral since the velocity is increasing) increasing)

Compared to a linear accelerator, this arrangement allows Compared to a linear accelerator, this arrangement allows a greater amount of acceleration in a more compact spacea greater amount of acceleration in a more compact space

Two hollow D shaped Two hollow D shaped electrodes exist in a electrodes exist in a vacuum. A uniform vacuum. A uniform magnetic field is applied magnetic field is applied perpendicular to the perpendicular to the plane of the “Dees”plane of the “Dees”

Charged particles are injected into a D, the magnetic field Charged particles are injected into a D, the magnetic field sets the particle on a circular path causing it to emerge sets the particle on a circular path causing it to emerge from the other side of this D & to enter the next.from the other side of this D & to enter the next.

As the particle crosses the gap between the Ds the As the particle crosses the gap between the Ds the supplied current changes direction (high frequency AC) & supplied current changes direction (high frequency AC) & the particle is accelerated, (causing a larger radius) the particle is accelerated, (causing a larger radius)