Comprehension CheckComprehension Check

1.1. An electron is moving at right angles to An electron is moving at right angles to uniform magnetic field; if the electron is uniform magnetic field; if the electron is moving at .010c, determine the moving at .010c, determine the magnitude of the force if:magnitude of the force if:

1.1. B = 51 000nT (~Earth’s magnetic field)B = 51 000nT (~Earth’s magnetic field)

2.2. B = 5.0mT (~fridge magnet)B = 5.0mT (~fridge magnet)

3.3. B = 1.0T (~rare earth magnet)B = 1.0T (~rare earth magnet)

4.4. B = 3.0T (~superconducting magnet)B = 3.0T (~superconducting magnet)

Comprehension CheckComprehension Check

1.1. F = 2.5x10F = 2.5x10-17-17NN

2.2. F = 2.4x10F = 2.4x10-15-15NN

3.3. F = 4.8x10F = 4.8x10-13-13NN

4.4. F = 1.4x10F = 1.4x10-12-12NN

Charged Particle Applications Charged Particle Applications and Torqueand Torque

Physics 12Physics 12

Force on a Current Carrying Wire in Force on a Current Carrying Wire in a Magnetic Fielda Magnetic Field

Take the equation for the force Take the equation for the force experienced by a charged particle moving experienced by a charged particle moving in a magnetic field and the definition of in a magnetic field and the definition of current to develop an equation for a current to develop an equation for a current carrying wire in a magnetic fieldcurrent carrying wire in a magnetic field

BIF

TorqueTorque

Torque is the cross Torque is the cross product of radius and product of radius and forceforce

The units are Nm but The units are Nm but are not joules!are not joules!

The direction is The direction is positive for ccw and positive for ccw and negative for cwnegative for cw

sinrF

Fr

Torque on a Current Carrying LoopTorque on a Current Carrying Loop

GalvanometerGalvanometer

The force experience by The force experience by a current carrying wire in a current carrying wire in a magnetic field can be a magnetic field can be used to build a used to build a galvanometergalvanometerBased on the length of Based on the length of wire, the strength of the wire, the strength of the field, the tension in the field, the tension in the spring and the current, spring and the current, different readings are different readings are obtainedobtained

Charged Particle placed in a B-Charged Particle placed in a B-FieldField

When a charged particle is placed in a When a charged particle is placed in a magnetic field, it experiences a force magnetic field, it experiences a force based on the cross product of its velocity based on the cross product of its velocity and the magnetic field intensityand the magnetic field intensityTherefore, a charged particle experiences Therefore, a charged particle experiences no force if it is not movingno force if it is not moving

Circular MotionCircular Motion

When a charged particle is moving in a When a charged particle is moving in a magnetic field, it always experiences a magnetic field, it always experiences a force that is at right angles to the velocityforce that is at right angles to the velocity

This results in a change in the direction of This results in a change in the direction of the velocity but not its magnitudethe velocity but not its magnitude

As a result, this force will provide a As a result, this force will provide a centripetal acceleration towards the centre centripetal acceleration towards the centre of the circular pathof the circular path

How can we calculate centripetal How can we calculate centripetal acceleration?acceleration?

r

va

t

v

r

v

v

v

r

tv

tvr

tvdv

v

r

r

c

2

2

Centripetal ForceCentripetal Force

Like the centripetal Like the centripetal acceleration, the acceleration, the centripetal force is always centripetal force is always directed towards the directed towards the centre of the circlecentre of the circle

The centripetal force can The centripetal force can be calculated using be calculated using Newton’s Second Law of Newton’s Second Law of MotionMotion

r

mvF

r

va

amF

c

c

2

2

Charged Particle moving in an B-Charged Particle moving in an B-FieldField

A charged particle, A charged particle, moving with an initial moving with an initial velocity enters a velocity enters a magnetic field as shown magnetic field as shown in the diagram at the in the diagram at the right and will follow a right and will follow a circular path as a result circular path as a result of the b-fieldof the b-fieldWe can solve this We can solve this problem through the use problem through the use the centripetal motionthe centripetal motion

Lorentz Force and Velocity Lorentz Force and Velocity SelectorSelector

The Lorentz Force The Lorentz Force gives the method of gives the method of calculating the total calculating the total force acting on the force acting on the charged particlecharged particleWhen the velocity is When the velocity is equal to the ratio of equal to the ratio of E/B, the particle E/B, the particle passes straight passes straight through the fields, through the fields, otherwise it is otherwise it is deflecteddeflected

BvqEqF

Mass SpectrometerMass SpectrometerA mass spectrometer can be built using a A mass spectrometer can be built using a velocity selector followed by an area of velocity selector followed by an area of uniform magnetic field. Particles that have uniform magnetic field. Particles that have the correct velocity will pass through the the correct velocity will pass through the velocity selector and into the magnetic field velocity selector and into the magnetic field where they will be curved.where they will be curved.

Develop an equation that will allow you solve Develop an equation that will allow you solve for the ratio m/q based on the magnetic field, for the ratio m/q based on the magnetic field, speed of the particle and radius of curvaturespeed of the particle and radius of curvature

v

rB

q

m 0

e/me/m

Thompson used a similar technique to Thompson used a similar technique to measure the ratio of charge to mass ratio measure the ratio of charge to mass ratio of electronsof electrons

Using variable electric and magnetic fields, Using variable electric and magnetic fields, it is possible to investigate the charge of it is possible to investigate the charge of the electron in comparison to its massthe electron in comparison to its mass

CyclotronCyclotron

In a cyclotron, a charged In a cyclotron, a charged particle is accelerated in particle is accelerated in an alternating electric field an alternating electric field and passes into an area of and passes into an area of uniform magnetic field uniform magnetic field which turns it in a circle which turns it in a circle and it passes back into the and it passes back into the magnetic fieldmagnetic fieldAs velocity increases, the As velocity increases, the radius gets larger and radius gets larger and largerlarger