Q

# 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

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$r=\frac{mv}{qB}=\sqrt{\frac{2mE}{qB}}$

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

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

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

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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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