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(a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle. (b) Draw a schematic sketch of a cyclotron. Explain, giving the essential details of its construction, how it si used to accelerate the charged particles. |
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Answer» Solution :(a) When a charged particle with charge q MOVES inside a magnetic field `vecbeta` with velocity v, it experiences a force, which is given by : `VECF=q(vecv^(xx)vecbeta)` Here `vecv` is perpendicular to `vecbeta`,`vecF` is the force on the charged particle which ACTS as the centipetal force and makes it move along a circular path.  Let m be the mass of the charged particle and r be the radius of the circular path. `therefore q(vecv^(xx)vecbeta)=mv^(2)` V and B are at right angles. `therefore "" qvB=(mv^(2))/(r)""therefore"" (mv)/(Bq)` TIME periodof circular MOTION of the charged particle can be calculated as shown below : `T=(2pir)/(v)=(2pi)/(v)(mv)/(Bq)rArrT=(2pim)/(Bq)` `therefore " Angular frequency is" omega=(2pi)/(T)"" therefore " " omega=(Bq)/(m)`. Therefore, the frequency of the revolution of the charged particle is independent ofvelocity or energy of the particle. (b)Cyclotron : |
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