A positively charged particle of charge 'q' enters in a uniform magnetic field B directed inward and is deflected a distance x after travelling a distance Y as shown in the figure. The magnitude of linear momentum of the particle is:

Options

A. `(qBY)/2`
B. `(qB)/2(x^2/Y+x)`
C. `(qB)/(2x)(x^2+Y^2)`
D. `(qB)/(2Y)(x^2+Y^2)`

Answer

C

Explanation

`R sin theta =Y`
`R(1-cos theta )=x`
`rArr (1-x/R)^2 + (Y/R)^2 =1 rArr R=1/(2x)(x^2+Y^2)`
`rArr p=mv=(qB)/(2x)(x^2+Y^2)`