|
|
Experiment to measure
the Charge to Mass Ratio of Electrons
| 1.
Preparation: |
a) |
Revise
the motion of charged particles in electric and magnetic fields. |
|
b) |
You must
know the meaning of the term "thermionic emission". |
|
c) |
See part
3 below. |
| 2. |
The
method proposed here is similar to that used by J.J. Thomson in
1897. Electrons in an evacuated tube (a "cathode ray
tube") are sent towards a region of space where there are
electric and magnetic fields at 90° to each other. If the field
strengths have a particular ratio
then charged particles can pass through them undeflected. |
|
|
| 3. |
In the following analysis
|
|
|
V = voltage
accelerating the electrons and producing the electric
field between the plates |
|
v = speed of
the electrons |
|
m = mass of
one electron and e = charge on one electron |
|
E = electric
field strength (E = V/d where d = distance between
plates) |
|
B = magnetic
flux density |
|
|
|
If the electrons pass undeflected
(magnitude of electric force equal to magnitude of magnetic force),
then it can easily be shown that
|
|
|
|
Verify this equation
for yourself.
|
|
To find the speed of the electrons,
remember that during acceleration the electrons are losing
electric P.E. and gaining K.E.
|
|
E.P.E. lost = K.E.
gained
|
|
eV = ½mv² |
|
| therefore |
v² = 2eV/m |
equation 2 |
|
|
Combining equations 1 and 2 to
eliminate v gives us
|
|
e/m
= ____________
|
|
| To
calculate the magnitude of the flux density
produced near the centre of two "Helmholtz
coils" |
|
B
= 0·72 µ0N I/r |
| where |
N
= number of turns on one coil |
|
I
= current |
|
r
= radius of coils |
|
µ0
= permeability of a vacuum = 1·257 × 10-6
Hm-1 |
| N,
I, r, V etc
can all be measured with reasonable
precision. |
| What
is the greatest source of error likely to be? |
| It
will probably be easier to answer this when you
have done the experiment. |
|
|
|
© David
Hoult 2008 |
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Open Door Web Site