JEE Advanced | 2017Magnetic field due to currentHard

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? 
             

Options

A.

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

B.

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

C.

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

D.

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

Solution


R'=pqB
(R' - R)2 + R2 = R'
  R'=138R

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