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Two particles $A$ and $B$ of same mass and having charges of same magnitude but of opposite nature are thrown into a region of magnetic field (as shown) with speed $v_{1}$ and $v_{2}$ $(v_{1} > v_{2})$ . At the time particle $A$ escapes out of the magnetic field, angular momentum of particle $B$ w.r.t. particle $A$ is proportional to (Assume both the particles escape the region after traversing half circle)

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$v_{1} + v_{2}$

${v_{1}}^{2} - {v_{2}}^{2}$

$v_{1} - v_{2}$

${v_{1}}^{2} + {v_{2}}^{2}$

answer is C.

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Detailed Solution

$L = m v r = m v (\frac{m v}{q B}) = \frac{m^{2} v^{2}}{q B}$

so $L_{1} - L_{2} = \frac{m^{2}}{q B} (v_{1}^{2} - v_{2}^{2})$

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