Cyclotron | class 12 physics | working principle and construction | cyclotron accelerator

Summary

The script introduces the cyclotron, a device with two semicircular metal 'dees' that accelerates particles using an alternating electric field and a perpendicular magnetic field. Protons or other positively charged particles are accelerated in a spiral path, gaining velocity with each pass through the dees, until they reach the periphery for experimental purposes. The key to its operation is synchronizing the high-frequency oscillator's frequency with the particle's revolution frequency, ensuring continuous acceleration without increasing the revolution period.

Takeaways

• 🔧 A cyclotron is composed of two semicircular metal boxes called dees with a small gap between them.
• 🔌 The dees are connected to a high tension oscillator, creating an alternating potential for particle acceleration.
• 💨 The cyclotron is enclosed in an insulated metal box with low-pressure gas to facilitate particle movement.
• 🧲 The apparatus is positioned between strong electromagnets to generate a perpendicular magnetic field to the dees' plane.
• ⚡ The initial stage involves a positively charged particle being accelerated by the negatively charged dee.
• 🌀 Inside the dee, the particle is influenced solely by the magnetic field and its pre-acquired velocity, causing it to turn in a circular path.
• 🔄 The high tension oscillator changes the polarity of the dees to provide a favorable electric field for further acceleration of the particle.
• 🔁 The particle's velocity increases with each pass between dees, resulting in a larger radius of its circular path due to the dependency on velocity.
• 🔄 The frequency of the high tension oscillator must match the particle's revolution frequency for continuous acceleration.
• ⏳ The time period of the particle's revolution is independent of the radius, contrary to what might be expected.
• 🚀 The particle eventually reaches the periphery of the dees, where it is deflected by a negative electrode onto a target for bombardment.

Q & A

What is a cyclotron and what are its main components?

A cyclotron is a type of particle accelerator that consists of two flat semicircular metal boxes called dees, a high tension oscillator, an insulated metal box containing low-pressure gas, and strong electromagnets providing a magnetic field perpendicular to the dees' plane.

How is the high-frequency alternating potential created in a cyclotron?

The high-frequency alternating potential is created by connecting the dees to the terminals of a high tension oscillator, which generates several million cycles per second between the dees.

What role does the magnetic field play in the operation of a cyclotron?

The magnetic field, provided by the electromagnets, acts perpendicular to the plane of the dees and influences the trajectory of the charged particles, causing them to move in a circular path.

Why is the gas inside the cyclotron's metal box kept at low pressure?

The low-pressure gas inside the insulated metal box reduces air resistance, allowing the accelerated particles to move more freely and maintain their velocity within the cyclotron.

How does a positive particle gain velocity inside a cyclotron?

A positive particle gains velocity by being accelerated by the electric field of a dee that is at a negative potential at that moment, and then entering another dee where the electric field is zero but the particle retains its velocity due to its momentum.

What is the significance of the dees' polarity changing in the cyclotron?

The polarity change of the dees, facilitated by the high tension oscillator, provides a favorable electric field that accelerates the positive particle each time it moves from one dee to another.

How does the radius of a particle's circular path relate to its velocity?

The radius of a particle's circular path is dependent on its velocity. According to the equation of the radius of a circular turn, an increase in velocity results in an increase in the radius.

Why is it crucial for the frequency of the high tension oscillator to match the frequency of the particle's revolution within the dee?

Matching the frequency ensures that whenever the charged particle is in the gap between the dees, the electric field is aligned with the particle's velocity, allowing for continuous acceleration.

How does the time period of a particle's revolution relate to the radius of its circular path?

Contrary to what one might expect, the time period of a particle's revolution in a cyclotron is independent of the radius of its circular path due to the specific dynamics of the cyclotron's operation.

What happens to the accelerated particle when it reaches the periphery of the dees?

Upon reaching the periphery of the dees, the accelerated particle is deflected by an auxiliary negative electrode onto the target to be bombarded.

What is the role of the auxiliary negative electrode in a cyclotron?

The auxiliary negative electrode is used to deflect the accelerated particle to the target at the periphery of the dees, allowing for the particle to be directed towards its intended point of impact.

Outlines

00:00

🔬 Cyclotron Structure and Working Principle

The first paragraph introduces the cyclotron, a particle accelerator consisting of two semicircular metal boxes called 'dees' with a small gap between them. Positioned near the center of the gap, a proton or a combination of proton and neutron is accelerated by the high-frequency alternating potential provided by the high tension oscillator. The dees are enclosed in an insulated metal box with low-pressure gas and placed between strong electromagnets, creating a magnetic field perpendicular to the dees' plane. The working mechanism involves the acceleration of a positive particle by the electric field when it is in the gap and then entering a dee where it moves in a circular path under the influence of the magnetic field. The particle's velocity increases with each turn, allowing it to move in larger semicircular paths. The frequency of the high tension oscillator must match the particle's revolution frequency for continuous acceleration.

05:01

🌀 The Constant Time Period of Cyclotron's Particle Revolution

The second paragraph clarifies a misconception regarding the time period of a particle's revolution in a cyclotron. Contrary to the expectation that an increase in the radius of the circular path would lead to an increase in the time period, the time period is actually independent of the radius. This is due to the fact that as the particle's velocity increases, allowing it to travel in larger circles, the magnetic field's influence compensates, maintaining a constant revolution frequency. The particle continues to accelerate and move in a spiral path until it reaches the periphery of the dees, where it is deflected by a negative electrode onto a target for bombardment. The paragraph concludes with a call to action for viewers to like, subscribe, and enable notifications for the channel.

Keywords

💡Cyclotron

A cyclotron is a type of particle accelerator that uses a magnetic field and an electric field to accelerate charged particles to high energies. In the context of the video, it is the main apparatus being discussed, and the script explains its components and the process of particle acceleration. The cyclotron's function is central to the video's theme of explaining how particles are accelerated to high velocities for various scientific applications.

💡Dees

Dees are the two flat semicircular metal boxes that are part of the cyclotron's structure. They are crucial for the acceleration process as they create an electric field that propels the charged particles. The script mentions that the dees are connected to a high tension oscillator, creating an alternating potential necessary for particle acceleration, and that they are arranged with a small gap between them where the particle starts its journey.

💡High Tension Oscillator

The high tension oscillator is a device connected to the dees of the cyclotron that generates a high-frequency alternating potential. This component is vital for the operation of the cyclotron as it provides the changing electric field needed to accelerate the particles. The script explains that the oscillator's frequency must match the particle's revolution frequency for efficient acceleration.

💡Magnetic Field

The magnetic field is generated by the strong electromagnets placed around the cyclotron and is essential for directing the path of the charged particles. As described in the script, the magnetic field acts perpendicular to the plane of the dees, causing the particles to move in a circular path due to the Lorentz force, which is a result of the charged particles' velocity being perpendicular to the magnetic field.

💡Gauss's Theorem

Gauss's theorem, also known as Gauss's law, is a fundamental principle in electromagnetism that states the electric field inside a conductor is zero. In the script, it is mentioned to explain why the particle inside a dee is only influenced by the magnetic field and its initial velocity, as the electric field inside the dee has no effect on it.

💡Left Hand Fleming Rule

The Left Hand Fleming Rule is a simple rule used to determine the direction of force on a current-carrying conductor in a magnetic field. The script uses this rule to explain how the force acts on the positive particle in the magnetic field, causing it to start turning in a circular path.

💡Semicircular Path

A semicircular path is the trajectory that the accelerated particle follows within the cyclotron due to the influence of the magnetic field. The script describes how the particle moves in a semicircular path of increasing radius as its velocity increases with each acceleration cycle.

💡Velocity

Velocity is a physical quantity that refers to 'the speed in a given direction.' In the context of the cyclotron, the script explains how the particle's velocity is increased by the electric field and how this increase in velocity leads to a larger radius of the semicircular path.

💡Time Period

The time period of revolution refers to the time it takes for the particle to complete one full circular path within the cyclotron. The script clarifies that contrary to what one might expect, the time period does not increase with the radius; it is independent due to the constant frequency of the oscillator matching the particle's revolution frequency.

💡Spiral Path

A spiral path is the overall trajectory of the particle as it is accelerated and moves outward from the center of the cyclotron towards the periphery. The script describes how the particle follows this path due to the combination of the circular motion within the dees and the constant acceleration provided by the electric field.

💡Auxiliary Negative Electrode

The auxiliary negative electrode is a component at the periphery of the dees that deflects the accelerated particle towards the target. This is the final stage of the particle's journey within the cyclotron, as described in the script, where the particle reaches extremely high velocities before being directed to interact with a target material.

Highlights

Introduction to the cyclotron, a device with two flat semicircular metal boxes called dees.

Dees are arranged with a small gap and connected to a high tension oscillator for high frequency alternating potential.

The cyclotron is enclosed in an insulated metal box with low-pressure gas.

The apparatus is placed between strong electromagnets to provide a magnetic field perpendicular to the dees' plane.

Working principle of the cyclotron begins with a positive particle at the center.

Acceleration of the positive particle by the negatively charged dee.

Influence of the electric field inside a conductor is zero, leaving the particle under magnetic field influence only.

The particle turns in a circular path due to the magnetic field, following the left-hand Fleming rule.

High tension oscillator changes polarity to provide a favorable electric field for particle acceleration.

The particle's velocity increases with each turn, leading to a larger radius in the next circular path.

The radius of the circular path is dependent on the particle's velocity.

The frequency of the high tension oscillator must match the particle's revolution frequency for efficient acceleration.

The time period of revolution is independent of the radius, a key feature of the cyclotron's operation.

The particle moves in a spiral path, gaining extremely high velocity.

An auxiliary negative electrode at the periphery of the dees deflects the accelerated particle towards the target.

The video concludes with an invitation to like, subscribe, and enable notifications for new content.

Transcripts

introduction to parts of cyclotron

the cyclotron consists of

two flat semicircular metal boxes

called dees

and are arranged with the small gap between them

A proton

or may be the combination of proton and neutron

is located near the mid point of the gap between the dees

the dees are connected to the terminals of high tension oscillator

so that a high frequency alternating potential

of several million cycles per second exists between the dees

the dees are enclosed in insulated metal box

containing gas at low pressure

The whole apparatus is placed between the strong electromagnets

such that

south pole of one electromagnet is facing downward

and north pole of another electromagnet is facing upward

which provides

a magnetic field perpendicular to the plane of the dees

acting from north pole to south pole

working of cyclotron

in the initial stage

a positive particle is at the center

the positive particle at the center

is accelerated by a dee which is at negative potential at that moment

the accelerated positive particle

with gain in velocity

enter s inside a dee

as we know

according to the Gauss theorem

influence of electric field inside a conductor is always zero

therefore,

now a positive particle inside a dee

is only in the influence of magnetic field

and velocity which it gains before

with velocity perpendicular to the magnetic field

therefore,

according to left hand flemming rule

force starts acting upon it

and positive particle in the magnetic field

starts turning in a circular path

with zero acceleration

after turning in a circular path

again positive particle enters in a gap between the two dees

as soon as positive partilce enters in a gap

high tension oscillator provides a favourable electric field

by changing the polarity of two dees

to accelerate the positive particle

because now electric field is favourable to positive particle

it again accelerated by the electric field

which increase its velocity

now it enters another section of dee

where electric field is zero

because of high velocity compared to previous circular turn

this time

positive particle will turn in a semicircular path of larger radius

as the equation of the radius of a circular turn

shows that

radius of a path of a positive particle

is dependent on the velocity of a positive particle

if the velocity will increase radius will also increase

every time when the positive particle

move from one dee to another dee

it is acted upon by the electric field

and the positive particle is accelerated

which also increases velocity of positive particle

every time when the positve particle

move from one dee to another dee

the condition of working of cyclotron is that

the frequency of high tension oscillator

must be equal to the frequency

of the revolution of positive particle within the dee

then only

whenever the charge is in the gap

the electric field is along the velocity

you may ask a question !

if radius is increased

then the time period of revolution should also increase

but its not true

because the equation of time period

of revolution of a positive particle

in a cyclotron

is independent of the radius of revolution of positive particle

in this way

positive particle starts moving in a spiral path

with extremely high velocity

till the positive particle reaches at the periphery of the dees

where an auxiliary negative electrode

deflects the accelerated particle

on the target to be bombarded

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