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

Answer:

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

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,

$a_p=\dfrac{qvB}{m_p}$  .........(1)

Acceleration of deuteron,

$a_d=\dfrac{qvB}{m_d}$   ..........(2)

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

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

$\dfrac{a_p}{a_d}=\dfrac{m_d}{m_p}$

$m_d=2m_p$

$\dfrac{a_p}{a_d}=\dfrac{2m_p}{m_p}\\\\\dfrac{a_p}{a_d}=2$

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