1)

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?

 1012020237_rrrr.PNG


A) 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 p2

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

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

D) For a fixed B, particles of same range 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

Answer:

Option B,C

Explanation:

a)

1012020205_axis.PNG

(b)

  r(1-cosθ)=R

   1012020772_QQ.PNG

rsinθ=3R2

sinθ1cosθ=32

2sinθ2cosθ22sin2θ2=32

cotθ2=32

tanθ2=23

tanθ=2(23)149=4359=125

1012020644_YYYY.PNG

sinθ=1213

r(1213)=3R2;r=13R8=PQB;B=8P13QR

(c) PQB<3R2,B>2P3QR

(d)  r=mvQB,d=2r=2mvQBdm