JEE Advanced 2017 Paper 2

For (A) For B=

8P

13QR

r=

P

QB

=

p13QR

Q8p

=

13R

8

Clearly x=√(

13r2

8

)−(

5R

8

)2
x=

3R

2

Hence particle enters region 3 through point P2 (r = radius of circle in which charge moves)

For (B) The particle will reenter region 1 if r<

3R

2

P

QB

<

3R

2

⇒B>

2p

3QR

For C Distance between point p1 and point of re-entry into region 1 = 2r
y=

2mv

qB

∝m
For (D) When particle re-enters region 1 through longest possible path, it will re-enter horizontally only.Hence at farthest point from y axis, if must be vertical with magnitude of momentum being p. hence change in its linear momentum must be √2p