How Does a Velocity Selector Work? Principle, Diagram & Real-World Examples
A Velocity selector is a region in which we will find a uniform electric and magnetic field, in other words, a region where the Electric force acting a charged particle will be equal to the magnetic field force. The velocity selector is an arrangement of electric and magnetic fields. This arrangement of the electric field and the magnetic field is used to select a charged particle of a certain velocity out of a beam containing charges moving with different velocities irrespective of their mass and charges.
What is Velocity Selector?
While studying the motion of charged particles in a uniform magnetic field, we learned that the charged particles will experience the force due to both electric and magnetic fields. Whenever we consider a beam of charges we know that all the charged particles will be possessing different velocities. We come across certain experiments where we want one particular charge with a particular velocity, to obtain such charged particles we use velocity selectors.
The velocity selector is an arrangement of electric and magnetic fields. The arrangement of the electric and magnetic fields is used to select a charged particle of a certain velocity out of a beam containing charges moving with different velocities irrespective of their mass and charges.
Let us consider a charged particle of charge q is moving with velocity v in uniform electric and magnetic fields such that the electric field, magnetic field, and the velocity of the charged particle are mutually perpendicular to each other. Let us consider the electric field to be along the y-direction, the magnetic field along the z-direction, and the velocity of the charge be along the x-direction.
The charged particle considered will experience the force due to both magnetic and electric fields. We know that the force exerted on charge q is given by,
\[ \Rightarrow F_{e} = qE = qE \widehat{j} \]
Similarly, the force exerted by the magnetic fields is given by:
\[\Rightarrow F_{B} = q(V \times B) = q(v_{0}\widehat{i}\times B\widehat{k})=qv_{0}B(-\widehat{j})\]
Clearly, the electric force and magnetic force are opposite in direction. Now, for the velocity selector, we follow the condition where both forces must be equal to each other. Then from equation (1) and (2), we get,
\[\Rightarrow qE\widehat{j}=-qv_{0}B\widehat{j}\]
\[\Rightarrow v_{0}=\frac{E}{B}\]
In a velocity selector, charged particles must move with a speed of \[v_{0}=\frac{E}{B}\] in order to pass through the equipment. Hence, the velocity selector, as its name suggests, allows charged particles with a particular velocity to pass through (hence, selecting particles of a certain velocity). The mechanism of a velocity selector is shown in the below figure.
The velocity selector will have a uniform electric field and a uniform magnetic field. Consider a mechanism as shown in the figure, a uniformly charged electric field will be generated by a positively charged bottom plate and a negatively charged top plate. This will cause an electric field to form between the given two plates, that is pointing in the upward direction. And at the same time, a uniform magnetic field will also be generated between the plates. The uniform magnetic field can be directed inwards or outwards. In other words, the uniform magnetic field can be directed into the paper or out of the paper. In the figure above, the magnetic field is directed outwards.
In order for the charged particle to pass through space without being deflected (either upwards or downwards), the upwards force must be equal to the downwards force. If the positively charged particle has a slightly larger velocity than \[\frac{E}{B}\] , the particle will be deflected downwards due to the larger downwards force.
Solved Example
1. A Velocity Selector is Used to Select Alpha Particles of Energy 200KeV. From a Beam Containing Particles of Several Energies. The Electric Field Strength is 900 kV/m. What Must Be the Magnetic Field Strength?
Ans: The mass of an alpha particle is 6.68 x 10-27 kg. Thus, the velocity of the alpha particle is given by 3.095 x 106 m/s.
Therefore, the magnetic field strength for the particle moving with velocity 3.095 x 106 m/s we get,
\[\Rightarrow B=\frac{E}{v}\]
Where,
E - The strength of the electric field.
v - The velocity of charged particles
\[\Rightarrow B=\frac{900\times10^{3}}{3.095\times10^{6}}\] = 0.29T = 290mT
Therefore, the magnetic field strength is 290mT.
The Fields of Velocity Sector
Uniform electric field: This field is produced by the upper plate with the wrong sides and the lower plate with the positive sides. This cost leads to the formation of a platform facing upwards in the image.
Uniform magnetic field: This field is equally located between two charged plates so that it can be directed inward or outward.
Speed Selector Limits
The weight or charge of the particles is not considered before the filter has passed.
All uncharged particles pass through the filter.
How does the Velocity Selector work?
Lorentz power starts when the electric field, magnetic field, and charger field are intertwined and this causes the electric field and the magnetic field to operate differently. When there is a need for charged particles of a certain speed to pass through these intersecting fields consistently, the electric field and the magnets vary to gain strength as a result of these fields to balance. This condition is known as the speed selector.
Points to Keep in Mind
The speed field is the region in which the electric current operates in charged particles that will equal the magnetic field.
The compulsory reaction of charged particles due to electric and magnetic fields is known as the Lorentz field.
The weight or charge of the particles is not taken into account when determining the speed selector.
Speed selectors are ideal for situations where charged particles or a certain speed should be selected for a series of charged particles with different speeds.
Speed Selector Uses
The speed selector is used with most spectrometers to select newly charged particles of a certain speed for investigation.
It uses mathematical calculations where the opposing electrical and magnetic fields correspond to the speed of a molecule. This way it allows the particles to move at just the right speed.
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FAQs on Velocity Selector in Physics: Concept, Formula & Applications
1. What is a velocity selector and what is its main purpose in Physics?
A velocity selector, also known as a Wien filter, is a device that uses both a uniform electric field (E) and a uniform magnetic field (B), oriented perpendicular to each other. Its primary purpose is to allow only charged particles moving at a specific, single velocity to pass through undeflected, effectively filtering them from a beam of particles with a wide range of velocities.
2. What is the fundamental principle behind the working of a velocity selector?
The working principle of a velocity selector is based on the balancing of forces on a charged particle. A moving charge 'q' in the device experiences two forces: an electric force (Fₑ = qE) and a magnetic force (Fₘ = qvB). The fields are set up so that these two forces act in opposite directions. When the magnitude of the electric force equals the magnitude of the magnetic force, the net force on the particle is zero, and it passes through without any deviation.
3. How is the condition v = E/B derived for a velocity selector?
The derivation for the selected velocity is straightforward. For a charged particle to pass through undeflected, the electric force and the magnetic force must be equal in magnitude and opposite in direction.
1. The electric force is given by Fₑ = qE.
2. The magnetic force is given by Fₘ = qvB (since v is perpendicular to B).
3. For zero net force, we set the magnitudes equal: |Fₑ| = |Fₘ|.
4. This gives us qE = qvB.
5. By cancelling the charge 'q' from both sides, we arrive at the condition for the selected velocity: v = E/B.
4. What happens to particles that are moving too fast or too slow through a velocity selector?
Particles that do not meet the specific velocity condition (v = E/B) are deflected and filtered out.
- If a particle's velocity is too high (v > E/B), the magnetic force (Fₘ = qvB) becomes greater than the constant electric force (Fₑ = qE). The particle is then deflected in the direction of the magnetic force.
- If a particle's velocity is too low (v < E/B), the magnetic force is weaker than the electric force. The particle is then deflected in the direction of the electric force.
5. What are some important real-world applications of a velocity selector?
Velocity selectors are crucial components in several scientific instruments. Key applications include:
- Mass Spectrometers: They are used in devices like the Bainbridge mass spectrograph to ensure that all ions entering the main magnetic field chamber have the same initial velocity. This is essential for accurately separating ions based on their mass-to-charge ratio.
- Charged Particle Accelerators: They can be used to create a beam of particles that all have a very specific kinetic energy.
- Electron Microscopy: They help in producing a mono-energetic electron beam, which improves the resolution and quality of the images produced.
6. Why must the electric field, magnetic field, and particle velocity be mutually perpendicular in a velocity selector?
The mutually perpendicular arrangement is essential for the opposing forces to work correctly. The electric force (Fₑ) acts along the direction of the electric field (E). The magnetic force (Fₘ), according to the Lorentz force law, is perpendicular to both the velocity (v) and the magnetic field (B). For Fₑ and Fₘ to be directly opposite, E, B, and v must all be at 90-degree angles to each other. This setup ensures that the forces can perfectly cancel each other out for a specific velocity.
7. Can a velocity selector be used to filter neutral particles like neutrons? Explain why or why not.
No, a velocity selector cannot be used for neutral particles. The device's operation depends entirely on the forces exerted by electric and magnetic fields on a charged particle. The formulas for these forces are Fₑ = qE and Fₘ = qvB. For a neutral particle like a neutron, the charge 'q' is zero. Therefore, it will experience no electric or magnetic force and will pass through the device completely unaffected, regardless of its velocity.
