Magnetic Effects of Current and Magnetism Part 1

Let Fp,Fd and Fα be the forces and vp,vd and vα be the velocities of proton, deuteron and α−particle, respectively.
Since, F=Bqv
On dividing and multiplying F by m, we get
F=Bqv‌

m

m

⇒‌‌F=B‌

q

m

p‌‌(∵p=mv)
⇒‌‌F∝q∕m‌‌(∵p and B are same)
∴‌‌Fp:Fd:Fα‌‌=‌

+q

m

:‌

+q

2m

:‌

+2q

4m

‌
‌‌‌=1:1∕2:1∕2=2:1:1
‌‌ and ‌‌‌‌=Bqv
⇒‌‌∝F∕q
∴‌‌vp:vd:vα‌‌=‌

Fp

qp

:‌

Fd

qd

:‌

Fα

qα

=‌

2x

q

:‌

x

q

:‌

x

2q

‌‌=2:1:1∕2=4:2:1