The charge accelerator (sometimes known as an 'electron gun') used in
this simulation has been greatly simplified. It accelerates charged objects
by exerting an electric force upon them. The output of a real accelerator might
consist of thousands of objects of unknown mass, charge and velocity...
the output of this simulated accelerator is just one object, where you,
unlike the pioneers, know it's charge and mass. The energy lost by the
electric field becomes the kinetic energy of the charge.
The velocity selector (also known as a Wien filter) was developed
by Wilhelm Wien in 1898. It contains an electric field crossed with
a magnetic field in such a way that the only objects that can make
it through the filter in a straight line are ones that are charged,
and have a zero net force exerted on them (...the electric force is
equal and opposite to the magnetic force), regardless of the value of
the object's mass or the value of the object's charge. This occurs
when the velocity of the charged object is equal to E/B. Charged objects
that have a velocity that isn't equal to E/B have a curved path as they pass
through the filter.
Any charged object that passes through the hole in the right hand barrier
has successfully made it though the filter in a straight line, thus the
velocity of the charged object can be confirmed.
It now passes into a magnetic field, where the radius of the charged object's
object's path can be detected (a charged object will 'expose' photographic paper if
it hits the paper hard enough. The distance from the hole to the mark on the
paper can be measured; this distance is the diameter of the circlular path
of the charged object).
Knowing the the radius of this path, the speed of the charged object, and the
strength of the magnetic field, the 'charge to mass ratio', q/m, can be
found. This was, and is, an important calculation, as it led to to the
discovery of the charge and mass of the electron, which has had an
enormous impact on our lives. Which sounds difficult to believe, but
it's true :-).
K = mv ² / 2
W = VABq
FE = -VAB / d
FB = Bqv
∑F = (FE² + FB²)½ ∑F = ma ∆x = vi∆t + ½a∆t ² circumference = 2π r angle in radians = arc/radius sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent The shape of a charged object's path in the selector: In E-field only: parabola. In B-field only: circular. In crossed E and B fields: cycloid. Net force is zero: straight. FB = Bqv ∑F on a mass moving in a circle = mv ²/rFor the full screen simulation,
download this sim from kirbyx.com
K : kinetic energy of mass (joules) (J)
W : work done on charge by electric field (joules) (J)
m : mass of object (kilogram) (kg)
v : velocity of mass (meters/second) (m/s)
E : Electric field strength (volts/meter or newtons/coulomb) (V/m or N/C)
B : Magnetic field strength (tesla) (T)
VAB : voltage (a.k.a. electric potential difference) (volts) (V)
VA : electric potential at A (volts) (V)
VB : electric potential at B (volts) (V)
q : charge (coulombs) (C)
FE : electric force on charge (newtons) (N)
FB : magnetic force on charge (newtons) (N)
∑F : total force on charge (newtons) (N)
a : acceleration of mass (meters/second²) (m/s²)
r : radius (meters) (m)
∆x : change in position (meters) (m)
vi : initial velocity (meters/second) (m/s)
∆t : change in time (seconds) (s)
• To be calculator and student friendly, the range of values
chosen for this simulation have no exponents, unlike many
of the real-world values that are used for a real
mass spectrometer.
• For this simulation, there are no gravitational forces.
• In this simulation, a charged object will only pass through
the hole in the barrier if its path has been a continuous
straight line from the accelerator to the barrier.
• There is no motion in the z direction.
• Assume that there are no edge effects.
• This simulation is not to scale.