When charged particles enter a magnetic field perpendicularly, they feel a force which makes their path curve. A velocity selector selects charged particles for a specific velocity by using both an electric and magnetic field.
Equations
description
equation
Force on a particle in a magnetic field
F=BQv
Centripetal force
F=rmv2
Radius of particle path
r=BQmv
Velocity in a velocity selector
v=BE
Constants
constant
symbol
value
elementarycharge
e
1.6×10−19C
Variable definitions
quantity name
symbol
derived units
si base units
force
F
N
kgms−2
magneticfluxdensity
B
T
kgs−2A−1
velocity
v
ms−1
ms−1
charge
Q
C
As
radius
r
m
m
mass
m
kg
kg
elecricfieldstrength
E
Vm−1
kgmA−1s−3
Force on a charged particle
When a particle beam moves perpendicularly through a magnetic field it feels a force. The force is also perpendicular to the velocity of the particle, and therefore the particle has a curved path.
1.
Particle beam trajectory
2.
B field going into screen
The force can be calculated using the following equation:
F=BIL
By substituting in the following:
L=vtI=tQ
The following equation can also be obtained for the force acting on a single particle:
F=BQv
If the particles in the beam are electrons or protons this can be turned into:
F=Bev
Where e is the elementary charge.
Note: These equations are for the force acting on a single particle. You would need to multiple the equations by N for N particles. You can also calculate the acceleration of a particle by using Newton's second law, F=ma.
Example
A proton enters a magnetic field with a magnetic flux density of 0.25T. What is the force acting on the proton if it has a speed of6×104ms−1?
Firstly, write down what you know:
B=0.25Tv=6×104ms−1
Next, write down the equation for the force acting on a particle in a magnetic field:
F=BQv
Since the particle is a proton:
F=Bev
Substitute the values into the equation and calculate the force:
F=0.25×1.6×10−19×6×104=2.4×10−15N
The proton felt a force of 2.4×10−15Nacting on it.
Going in circles
Since the path of the particles is circular, they must feel a centripetal force:
F=rmv2
The magnetic force provides the centripetal force on the particle which means that they can be equated. Doing so allows you to find an expression for the radius of the path taken by the particles:
rmv2=BQv
r=BQmv
Velocity selector
A velocity selector is a device that selects charged particles for a specific velocity by using an electric and a magnetic field. It looks like the following:
1.
Vacuum chamber
2.
Path of particles with speed v
3.
Particle
4.
Magnetic force
5.
Electric force
6.
Straight direction of motion
The plates produce an electric field with field strength E which is perpendicular to a magnetic field with flux density B. When particles enter the chamber, they are acted upon by both of these fields and will deflect in different directions. This deflection will cancel, but only for particles with a specific velocity and will keep a straight path.
The reason why these particles aren't deflected is, due to their velocity, the magnetic force acting on them is equal to the electric force.
FB=FE
You can then substitute these forces and rearrange to find the selected velocities:
BQv=EQv=BE
Thus, the velocity of the selected particles can be regulated by changing the electric and magnetic fields.
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Motion of charged particles in an electric field
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Charged particles in a magnetic field
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FAQs - Frequently Asked Questions
What is a velocity selector?
A velocity selector is a device that selects charged particles for specific velocities using both an electric and magnetic field.
Why are particles with a specific velocity selected in a velocity selector?
In a velocity selector only specific particles are selected because due to their velocity the electric force acting on them is the same as the magnetic force.
What happens to a charged particle in a magnetic field?
If a particle moves perpendicularly to a magnetic field it will feel a force which will curve its path.