Derive an expression for maximum energy gained by the positive ion using a cyclotron.

Asked by Topperlearning User | 8th May, 2015, 10:46: AM

Expert Answer:

If ν= maximum velocity

and r= maximum radius of the circular path, followed by the positive ion in cyclotron.

 begin mathsize 11px style fraction numerator mν subscript 0 superscript 2 over denominator straight r subscript 0 end fraction space equals space Bqν subscript 0
straight nu subscript 0 space equals space Bqr subscript 0 over straight m end style

  

Where, B is the strength of magnetic field.

And, m and q are the mass and charge of positive ion respectively.

Then maximum energy acquired by the ion.

begin mathsize 11px style straight E subscript max space equals space 1 half mν subscript 0 superscript 2 space equals space 1 half straight m space open parentheses Bqr subscript 0 over straight m close parentheses squared
straight E subscript max space equals space fraction numerator straight B squared straight q squared straight r subscript 0 superscript 2 over denominator 2 straight m end fraction
end style

          

Answered by  | 8th May, 2015, 12:46: PM