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Solve! An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, ra respectively in a uniform magnetic field B. The relation between re, rp, ra is :

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, ra respectively in a uniform magnetic field B. The relation between re, rp, ra is :

  • Option 1)

    re < ra < rp
     

  • Option 2)

     re > rp = ra
     

  • Option 3)

    re < rp = ra
     

  • Option 4)

    re < rp < ra

 
Answers (1)
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r=\frac{mv}{qB}=\sqrt{\frac{2mE}{qB}}

\frac{\sqrt{m_{\prec }}}{q_{\prec }}=\frac{\sqrt{m_{p}}}{q_{p}}> \frac{\sqrt{m_{e}}}{q_{e}}

\therefore r_{\prec }=r_{p}> r_{e}

 

Radius of charged particle -

r=\frac{mv}{qB}=\frac{P}{qB}=\frac{\sqrt{}2mk}{qB}=\frac{1}{B}\sqrt{}\frac{2mV}{q}

-

 

 


Option 1)

re < ra < rp
 

This is incorrect

Option 2)

 re > rp = ra
 

This is incorrect

Option 3)

re < rp = ra
 

This is correct

Option 4)

re < rp < ra

This is incorrect

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