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# Velocity Selector

## Introduction of Velocity Selector

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

1. What is the velocity selector formula?

In the velocity selector, charged particles must move with a speed of $v_{0}=\frac{E}{B}$ to pass through the equipment. This is also known as the velocity selector formula. Velocity selector is on its way to utilize completely the principle of motion of a charge in a magnetic field that is uniform. Particles will come out to be undeflected only when the velocity equals the ratio of $\frac{E}{B}$. This is a very important concept for the students to learn and adapt to through which they will attain some knowledge about the velocity vector.

2. What is velocity selector physics?

The velocity selector physics will have a uniform electric field and a uniform magnetic field. A uniformly charged electric field is 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 are pointing in the upward direction. And the uniform magnetic field is generated between the plates. The uniform magnetic field can be directed either inwards i.e., into the paper or outwards i.e., out of the paper.

3. How to use a velocity selector?

The Wien filter, also known as a velocity filter, is a device that combines precise and magnetic fields that can be used as a speed filter for charged particles, for example, electron microscopes and spectrometers. It is used in accelerator mass spectrometry to select particles based on their speed. The device is made up of electric or magnetic fields so that particles at the right speed will not be affected while other particles will deviate. It can be configured as a rechargeable particle power converter, monochromatic, or mass spectrometer.

4. How to apply the speed selection principle to the bainbridge mass spectrograph?

A device called the Bainbridge mass spectrometer is used to determine atomic mass. When one or more electrons are released from an atom then it has a positive net charge and becomes a positive ion. Only ion-specific ions are allowed to exit the speed selector. The Bainbridge Mass Spectrometer is a tool used to accurately determine the number of atoms. Schematic diagram of this spectrometer. Atoms are released by one or more electrons, have a positive charge and become directions.

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