6.3.2 Motion of Charged Particles

Explain the following

-When fields point in the same direction, fields add up. Producing a stronger field

-When the point in the opposite direction, it cancels, so a weaker field is formed

-Strong field down and weaker field up causes the wire to be pushed upwards

Describe the trajectory of a charged particle in a uniform magnetic field

Charged particles follow a circular path in a magnetic field

Why do charged particles follow a circular path in a magnetic field

Because the magnetic force is perpendicular to velocity and acts as a centripetal force

How to calculate the force on the charged particle travelling at right angles to a uniform magnetic field

F=BQv

F= force (N)

B= magnetic flux density (T)

Q= Charge (C)
v= velocity (ms^-1)

How can a velocity selector choose e- with a desirable speed

• The source produces e- with a variety of speeds

• Electric and magnetic fields are perpendicular

• e- experiences: Electric force (F= qE) upwards and magnetic force downwards (F=Bqv)

• The electric force is constant

• Magnetic force is higher in faster-moving electrons

• if F_E=F_B electron passes straight through (these are the electrons with the wanted velocity!)

• if F_B>F_E, e- deflects downwards

• if F_E>F_B, e- deflects upwards

Show that the speed of electrons chosen by the selector is given by v=E/B

F=Bqv
F=qE

Bqv=qE

v=E/B

How to adjust the wanted speed of the e-

v=E/B

Increasing B, would target slower electrons

Decreasing B, targets faster electrons

What happens to the chosen speed of e- is the p.d. across the plates is increased

The electric force increases, which is directly proportional to the velocity of e-

So the selector chooses faster electrons

How does a spectrometer work

• A source fires ions into a velocity selector

• Ions with the wanted speed pass through the selector

• So, now all the ions have the same speed ( v=E/B)

• Ions now move into a strong perpendicular magnetic field with a known magnetic flux density

• In the magnetic field, they travel on circular paths until they hit a detector

• The distance from where they enter the field to where they hit the detector is 2r (measuring this the radius can be found)

How can a spectrometer measure the charge: mass ratio (q/m) of ions that travel through it

F= Bqv F= mv²/r
Bqv= mv²/r
r= mv/Bq
rBq=mv
rB/v=m/q
v/rB=q/m

Why is it important for all the ions to have the same speed

So, the only thing affecting the q/m ratio is the mass.
A variable speed affects the ratio