An electron and a proton having same momenta enter perpendicular into a magnetic field then

An electron and a proton having same momenta enter perpendicular into a magnetic field then
  1. they will move undeflected
  2. curved path of electron and proton will be same. (Neglect sense of revolution)
  3. curved path of electron is more curved than proton
  4. path of the proton is more curved

Solution

The radius of curvature of a charged particle of mass $m$ and charge $q$ moving in a region with uniform perpendicular field $B$ is given by, $r=\frac{m v}{B q}=\frac{p}{B q}$ where, $p$ is the momentum of the charged particle. Since momenta are same and masses for electron and proton are different, so they will attain different velocities and hence experience different forces. But the radius of circular path is depending on momenta so both will be moving on same trajectory (curved path, neglecting the sense of revolution). :

Asked in: MHT CET 2022 (10 Aug Shift 2)

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