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Q.

The region has constant magnetic field as shown in the figure. A charged particle having mass $m$ and positive charge $q$ moving parallel to $x$ -axis as shown in the figure enters magnetic field of region $P$ (lies above $x$ -axis) with speed $v_{0}$ at point $X$ and comes out with speed $v_{1}$ from point $Y$ of magnetic field of region $Q$ (lies below $x$ -axis).
(Given, $d = \frac{m v_{0}}{2 B_{0} q}$ and $D = \frac{3 \sqrt{3} m v_{0}}{4 B_{0} q}$ ), Choose the correct option(s).

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a

$θ = 60 ° and v_{1} = \frac{v_{0}}{2}$

b

$θ = 90 ° and v_{1} = v_{0}$

c

Co-ordinates of centre of first circular path will be $(0, - \frac{m v_{0}}{2 B_{0} q}, 0)$

d

$θ = 60 ° and v_{1} = v_{0}$

answer is B, C.

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Detailed Solution

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Speed will remain unchanged

$v_{1} = v_{0}$

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The region has constant magnetic field as shown in the figure. A charged particle having mass m and positive charge q moving parallel to x -axis as shown in the figure enters magnetic field of region P (lies above x-axis) with speed v0 at point X and comes out with speed v1 from point Y of magnetic field of region Q (lies below x -axis).(Given, d=mv02B0q and D=33mv04B0q ), Choose the correct option(s).