A deuteron,with the same charge but twice the mass of a proton,moves with a speed of 6.0 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.20 T.Which of the paths described below would it follow? (q_p = 1.6 × 10−¹⁹ C and m_d = 3.34 × 10−²⁷ kg) A) a circular path of 6.3-cm radius B) a circular path of 1.6-cm radius C) a circular path of 3.1-cm radius D) a straight line path

Question

Quizplus · Accepted Answer

The magnetic force on a charged particle moving perpendicular to a magnetic field is given by F = qvB, where q is the charge of the particle, v is its speed, and B is the magnetic field strength. The force is perpendicular to both v and B, so it causes the particle to move in a circle. The radius of the circle is given by r = mv/qB, where m is the mass of the particle. In this case, the particle is a deuteron, which has a charge of +e and a mass of 2mp. So, the radius of the circle is:r = mv/qB = (2mp)(6.0 × 10^5 m/s)/(1.6 × 10^-19 C)(0.20 T) = 6.3 cmTherefore, the correct answer is A: a circular path of 6.3-cm radius.

A Deuteron,with the Same Charge but Twice the Mass of a Proton,moves