Velocity Selector: Formula, Fields, Limitations and Numericals

Velocity selector is a region where electric force acting on a charged particle is equivalent to magnetic field force on the same particle. Thus a velocity selector is ideal for exploiting the principle of motion of a charge in a uniform magnetic field. This principle is utilized to select a charged particle with certain velocity from a beam consisting of charges travelling with different velocities irrespective of their mass and charges.

Keyterms: Velocity, Magnetic Field Force, Electric Force, Magnetic force, Electromagnetic Field, Lorentz force, Magnetic Field, Spectrometry, Electric field

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Definition of Velocity Selector

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Velocity Selector is a specialized device consisting of perpendicular electric and magnetic fields used to select charge particles of certain velocity. These devices are primarily used in accelerator mass spectrometry for selecting particles based on their speed. When there is a requirement of a particular charge with a particular velocity from a beam of charges possessing different velocities, we use velocity selectors.

• The concept of velocity selector can be used as the arrangement of any electrical field as well as any megnetic field.
• Therefore, this electrical and magnetic force need to be uniform.

Velocity Selector

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Velocity Selector Formula

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Since for a velocity selector, both electric and magnetic forces must be equal to each other, we get,

⇒qE\(\vec{j}\)=−q\(v_{0}\)B\(\vec{j}\)

⇒\(v_{0}\)=\(\frac{E}{B}\)

where q is the charged particle

v is the velocity of the charged particle

Also Read:

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Lorentz Force

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It is defined as the force generated due to electromagnetic fields generated by a combination of electric and magnetic force on a point charge.

Lorentz Force formula for a charged particle:

F = q (E + v ∗ B)

where F is the force acting on the particle

q is the electric charge of the particle

v is the velocity

E is the external electric field

B is the magnetic field

Read More: Synchrotron

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How does Velocity Selector Works?

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The Lorentz force comes into play when electric field, magnetic field and motion of charge are perpendicular to each other and this results in forces due to electric field and magnetic field to act in opposite directions. When there is a need for charged particles of certain velocity to pass through these cross fields undeflected, electric field and magnetic field are varied to get forces due to these fields to be equal. This phenomenon is known as velocity selector.

1. Let us consider a charged particle q moving with velocity v. The force experienced by this particle due to electric field and magnetic field is represented by F = q (E + v × B) = FE + FB

2. 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. If the electric and magnetic forces are perpendicular to each other and also, perpendicular to the velocity of the particle, we have- 

Fe=qE=qEjˆ equation (1)

Force exerted by the magnetic field is given by:

FB=q(V×B)=q(v0iˆ×Bkˆ)=qv0B(−jˆ) equation (2)

3. Since for a velocity selector, both electric and magnetic forces must be equal to each other, thus from equation (1) and equation (2) we get,

⇒qE\(\vec{j}\)=−q\(v_{0}\)B\(\vec{j}\)

⇒\(v_{0}\)=\(\frac{E}{B}\)

Thus in a velocity selector, charged particles must move with a speed of v0= E/B to pass through the equipment.

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Fields of Velocity Selector

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Velocity Selector is applicable in the following two fields:

Uniform electric field: This field is generated due to negative charges of the top plate and positive charges of the bottom plate resulting in upward direction of the resultant field.

Uniform magnetic field: This field is generated between two charged plates and is present uniformly between the plates and can be directed either inwards or outwards.

Read More: Derivation of lorentz transformation

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Limitations of Velocity Selector

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Following are the limitations of velocity selector:

• Velocity Selector does not consider either the mass or charge of particles before passing through the filter.
• Velocity Selector allows all uncharged particles to pass through the filter.

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Numericals on Velocity Selector

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In velocity selector, charged particles must move with a speed of v₀ = E/B in a magnetic and electric field perpendicular to each other in order to pass through the equipment.

A velocity selector is used to select alpha particles of energy 200KeV from a beam consisting of particles having varied energies. The electric field is of 900 kV/m strength. Determine the magnetic field strength?

Since alpha particles are selected, the mass of an alpha particle is 6.68 x 10^-27 kg. So its velocity is 3.095 x 10⁶ m/s.

Since B=E/v

Where E = strength of the electric field

v = velocity of charged particles

⇒B= (900×10³)/ 3.095 x 10⁶

= 290mT

So the magnetic field strength is 290mT.

Also Read:

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Things to Remember

• Velocity sector is a region where electric force acting on a charged particle will be equal to the magnetic force.
• Force experienced by a charged particle due to electric and magnetic fields is known as the Lorentz field.
• Neither the mass nor the charge of particles is taken into consideration during determination of velocity selector.
• Velocity selectors are ideal in situations where a charged particle or certain velocity is to be selected from a stream of charged particles possessing different velocities.

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Previous Year Questions

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