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Velocity Selector

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A Velocity selector is a region in which we will find 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 charged 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.


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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.


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.

FAQ (Frequently Asked Questions)

1. What is the Velocity Selector Formula?

Ans: In the velocity selector, charged particles must move with a speed of v0 = E/B  in order to pass through the equipment. This is also known as the velocity selector formula.

2. What is Velocity Selector Physics?

Ans: 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 is 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.