Motion In Straight Line

Question

An alternating electric field of frequency v is applied across the dees (radius =R ) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it are given by

$straight B space equals mv over straight e and space straight K equals 2 mπ squared straight v squared straight R squared$
$straight B equals fraction numerator 2 πmv over denominator straight e end fraction space and space straight K space equals straight m squared straight pi space straight R squared$
$straight B equals space fraction numerator 2 πmv over denominator straight e end fraction space and space straight K space equals 2 mπ squared straight v squared straight R squared$
$straight B space equals mv over straight e space and space straight K space equals straight m squared πR squared$

Solution

straight B equals space fraction numerator 2 πmv over denominator straight e end fraction space and space straight K space equals 2 mπ squared straight v squared straight R squared

Frequency space straight v space equals fraction numerator eB over denominator 2 πm end fraction KE space equals space 1 half space mv squared space and space radius space straight R space equals space mv over eB Here comma space velocity space straight v space equals space fraction numerator πR over denominator straight T divided by 2 end fraction space equals space fraction numerator 2 πR over denominator straight T end fraction space equals space 2 πRv therefore space Radius space straight R space equals space fraction numerator straight m space left parenthesis 2 πRv right parenthesis over denominator eB end fraction Magnetic space field space straight B space equals space fraction numerator 2 πmv over denominator straight e end fraction Kinetic space energy straight K space equals 1 half straight m left parenthesis 2 πRv right parenthesis squared space equals space 2 mπ squared straight v squared space straight R squared

Some More Questions From Motion in Straight Line Chapter

For Daily Free Study Material Join wiredfaculty