A uniform magnetic field B exists in the region between x = 0 and x = 3 R 2 (region 2 in the figure)…

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 P1y=-R. Which of the following option(s) is/are correct?

  1. For B=813pQR , the particle will enter region 3 through the point P2 on x -axis
  2. For B>23pQR , the particle will re-enter region 1
  3. 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
  4. 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 farthest point from y -axis is p2

Solution

For  B=813 pQR, radius of path

R'=pO.B=p×13QRQ8p=138R

Using pythagorous theorem,y=5R8

∴    particle will enter region 3 through point  P2 for B>23pQR

Radius of path <3PQRQ2p=32R

∴    Particle will not enter in region 3 and will re-enter region 1

Charge on momentum = 2p. When particle enters region 1 between entry point and farthest point from y-axis.

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Asked in: JEE Advanced 2017 (Paper 2)

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