$A$ uniform magnetic field $B$ exists in the region between $x=0$ and $x=\frac{3 R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along $x$-axis enters region 2 from region 1 at point $P_1(y=-R)$. Which of the following option(s) is/are correct?
Select ALL correct options:
A
For $B>\frac{2 P}{3 Q R}$, the particle will re-enter region 1
B
For $B=\frac{8}{13} \frac{P}{Q R}$, the particle will enter region 3 through the point $P_2$ on $x$-axis
C
For a fixed B, particles of same charge Q and same velocity v, the distance between the point $P_1$ and the point of re-entry into region 1 is inversely proportional to the mass of the particle.
D
When the particle re-enters region 1 through the longest possible path in region2, the magnitude of the change in its linear momentum between point $P_1$ and the farthest point from $y$-axis is $P / \sqrt{2}$.
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