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.