The cyclotron is a device used to accelerate heavy positive charged particles (like protons, deuterons and Alpha particles, etc) to the higher energies.
Principles of Cyclotron –
When a charged particle moves into an electric field and the magnetic field it will experience Lorentz force. If a body is placed inside the conductor it does not experience any electrostatic force. This principle is known as electrostatic shielding and while moving between electric field and magnetic field particle gets accelerated.
Construction of Cyclotron-
Cyclotron consists of two hollows semicircular Dee’s D1 and D2. A strong magnetic field is applied perpendicular to plane of Dee’s where Dee’s are placed in such a way that diameter of Dee’s apparel. An alternating electro motive force source is applied across the Dee’s. so that the electric field can be produced between the Dee’s. this whole system is placed in a vacuum container.
Working of Cyclotron-
Consider a charged particle having positive charge q who is released between the space at this are follow. These charged particles will enter with some velocity v in a Dee D2. As the electric field inside that dee is zero and the only magnetic field is present and velocity and magnetic field are perpendicular to each other. So the particle will move in a circular path.
Now, when particle will come out from d2 it will and space where the electric field is present. It will experience electric force and will get accelerated. At the same time, the polarity of electromotive force on Dee’s will also change which will always accelerate the particles. Now the particle will enter in D1 where it will be complete its circular path under the influence of magnetic force. This process is repeated and the energy of particle increases continuously. the condition in which particle will get maximum velocity which is the frequency of particle should be equal to the frequency of the alternating source. This condition is known as the resonance condition.
Note – In half-circle of particle energy gained by the particle in qv then in full circle energy change will be to 2qv.
Limitations of cyclotron-
- A cyclotron is not accelerated like particles because according to the special theory of relativity mass of moving particle with velocity v.
- Uncharged particles cannot be accelerated with the help of cyclotron.
Uses of Cyclotron-
- A cyclotron is used to bombard energetic particles during nuclear reactions.
- It is also used to plant charged particles or ions into solids to modify their properties.
- It is also used in hospitals to produce radioactive substances and this radioactive substance can be used in the diagnosis and treatment of the diseases.
Magnetic Force On A Current-Carrying Conductor Placed In A Uniform Magnetic Field –
Consider a current-carrying conductor of length l is placed in uniform magnetic field b. Let current ‘I’ is flowing to the conductor. as we know that while applying a potential difference across the ends of the conductor the free electrons in the conductor will move with the drift velocity. As the magnetic force on a charge q moving with velocity v in a uniform magnetic field is given by the multiplication of charge q and (VXB) vector.
Direction of magnetic force-
- Fleming’s left-hand rule- If the first two fingers of left-hand thumb are stretched in such a way that all the three will be in the position of mutually perpendicular to each other. Now if the first finger of the left-hand point towards the magnetic field b while the middle finger of the left-hand point towards the direction of the current I then the stretched thumb of the left hand will represent the direction of the magnetic force on the current-carrying conductor. This is Fleming’s left-hand rule.
- Right-hand palm rule- If fingers of the right hand are open and thumb is also stretched. If fingers of the right hand point out towards the magnetic field and the thumb is directed or point out towards the current then the direction which is perpendicular to the palm of the right hand will represent the direction of the magnetic force.
Magnetic Force Between Two Current-Carrying Parallel Conducting Wires –
Consider two infinitely long current-carrying wires which are placed parallel to each other at a distance d. Let the current i1 and i2 are flowing through the wires respectively then there will be a magnetic force acting between the wires. Current i1 will be flowing through the wire one while from were to current it will be flowing.