Question

The ratio of radii of the circular paths of a proton and a deuteron when projected perpendicular to the direction of a uniform magnetic field with the same speed is

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 4 : 1
• E. 1 : 4

Hint:

The radius of the circular path in a magnetic field depends on the mass and charge of the particle. For the same charge and velocity, the radius is inversely proportional to the mass of the particle.

Answer 1

The Correct Option is B

The radius $r$ of the circular path of a charged particle moving in a magnetic field is given by the formula: $$r = \frac{mv}{qB}$$ where:
- $m$ is the mass of the particle,
- $v$ is the speed of the particle,
- $q$ is the charge of the particle,
- $B$ is the magnetic field strength. 
For a proton, $m_p$ and charge $q_p = e$, and for a deuteron, $m_d = 2m_p$ and charge $q_d = e$. 
Since both particles are moving with the same speed and in the same magnetic field, the ratio of the radii is: $$\frac{r_p}{r_d} = \frac{\frac{m_p v}{eB}}{\frac{2m_p v}{eB}} = \frac{1}{2}$$ Hence, the correct answer is (B) 1 : 2.