A deuteron is moving with a speed of 2.0 × 10⁶ m/s at right angles to a magnetic field. The field is uniform, with magnitude B = 0.40 T. The mass and charge of a deuteron are 3.3 × 10^-27kg and 1.6 × 10^-19 C, respectively. The radius of the deuteron orbit is approximately

Question

Quizplus · Accepted Answer

The radius of the orbit can be found using the formula for the centripetal force on a charged particle moving in a magnetic field:

F = qvB

where F is the centripetal force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength. This force is provided by the electrostatic force between the positively charged deuteron and the negatively charged electrons in the magnetic field.

The centripetal force is also given by

F = mv^2 / r

where m is the mass of the deuteron and r is the radius of the orbit.

Setting these two equations equal to each other and solving for r, we get

r = mv / qB

Plugging in the given values, we get

r = (3.3 × 10^-27 kg)(2.0 × 10^16 m/s) / (1.6 × 10^-19 C)(0.40 T)

r = 0.104 m

which is approximately 10 cm. Therefore, the correct answer is D.

A Deuteron Is Moving with a Speed of 2