Question

A proton and a deuteron are moving with equal velocities perpendicular to a uniform magnetic field. A deuteron has the same charge as the proton but has twice its mass. The ratio of the acceleration of the proton to that of the deuteron is:

a) 2

b) 1/2

c)There is no acceleration for proton and deutron

d) 1

e) 4

Answer 1

The ratio of the acceleration of the proton to that of the deuteron is 2

Step-by-step explanation:

For a moving charge in magnetic field, the magnetic force is balanced by force due to its motion. So,

`qvB=ma`

Acceleration of proton,

`a_p=(qvB)/(m_p)` .........(1)

Acceleration of deuteron,

`a_d=(qvB)/(m_d)` ..........(2)

Since, a deuteron has the same charge as the proton but has twice its mass.

Dividing equation (1) and (2) we get :

`(a_p)/(a_d)=(m_d)/(m_p)`

`m_d=2m_p`

`(a_p)/(a_d)=(2m_p)/(m_p)\\\\(a_p)/(a_d)=2`

So, the ratio of the acceleration of the proton to that of the deuteron is 2. Hence, the correct option is (a).