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Question

A uniform magnetic field B exists in the region between x=0 and x=3R2 (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 P1(y=R). Which of the following option(s) is/are correct?


A

For B=813pQR, the particle will enter region 3 through the point P2 on x-axis

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B

For B>23pQR, the particle will re-enter region 1

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C

When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linerar momentum between point P1 and the farthest point from y-axis is p/2

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D

For a fixed B, particles of same charge Q and same velocity v, the distance between the point P1 and point of re-entry region 1 is inversely proportional to the mass of the particle

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Solution

The correct option is B

For B>23pQR, the particle will re-enter region 1


When B=8p13QR

mv2r=Qv(8p13QR)r=13R8



Also CP2=CO2+OP22
=(5R8)2+(3R2)2

CP2=13R8

Thus the particle will enter region 3 through the point P 1 on X-axis
So, 'A' is the correct option.

For the charge +Q to return region 1 , the radius of the circular path taken by charge should be 3R/2

mv2(3R/2)=QvB2p3R=QB

B=2p3QR

i.e., B should be equal or greater than 2p2QR

'B'is the correct option.

Change in momentum =2p.
Thus 'C' is incorrect

Further
mv2r=qvBr=mvqBorrm

So 'D' is incorrect.

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