A proton moving in perpendicular magnetic field possess energy $E$. The strength of magnetic field is…

A proton moving in perpendicular magnetic field possess energy $E$. The strength of magnetic field is increases four times. But the proton is constrained to move in the path of same radius. The kinetic energy of proton will increase
  1. 4 times
  2. 12 times
  3. 8 times
  4. 16 times

Solution

\(r=\frac{\mathrm{mv}}{q B}=\frac{\sqrt[2]{2 m E}}{q B} E \propto B^2\) If \(B\) increases 4 times \(E\) becomes to 16 times

Asked in: MHT CET 2022 (06 Aug Shift 2)

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