Magnetic Effects of Current and Magnetism Part 1

Given, the charge on the proton, qp=+e
The charge on the alpha particles, qa=+2e
The expression of the radius of the orbit,
r=‌

mv

qB

⇒r=‌

p

qB

  (∵p=mv)
∵‌‌‌

rp

rα

=‌

pp

qp

×‌

qα

pα

⇒‌‌‌

2

1

=‌

+2e

+e

×‌

Pp

pα

[∵‌

rρ

rα

=‌

2

1

]
⇒‌‌‌

pp

pa

=1
Since, kinetic energy and momentum are related as
K=‌

p2

2m

∴‌

Kp

Kα

=‌

pp2mα

mppα2

⇒‌

Kp

Kα

=‌

mα

mp

=‌

4mp

mp

⇒‌

Kp

Kα

=‌

4

1