An electron and a proton move in circular orbits in a plane perpendicular to a uniform magnetic field B > . Find the ratio of the radii of their circular orbits when the electron and the proton have (a) the same momentum and (b) the same kinetic energy.

a)  ratio of radii for same momentum  = 1

b)   ratio of radii for same energy           = 2.3 ×

Explanation:

using formula  for radius

                            r =  

                       where m is mass

                        v is velocity

                        q is charge

                        B is magnetic field

a) for same momentum radius will be inversely proportional to                                              roduct of charge and magnetic and magnetic field

                       r ∝  

  since for proton and electron s charge and magnetic field is same so

b) using relation b/w kinetic energy and momentum

                 p =   ............(1)

where p is momentum and

   K.E is kinetic energy

 we know  

                  =

 from first equation  

since qB is same for electron and proton and energy is also         same(given)  

so we get

b.a device that inputs heat into a cool object