A proton starting from rest travels through a potential of 1.0 kV and then moves into a uniform 0.040-T magnetic field. What is the radius of the proton's resulting orbit? (m_proton = 1.67 × 10^-27 kg,e = 1.60 × 10^-19C) A) 0.080 m B) 0.11 m C) 0.14 m D) 0.17 m

Question

Quizplus · Accepted Answer

First, we can use the formula for the speed of a particle moving through a potential difference V:

v = sqrt(2eV/m)

where e is the charge of the particle, m is its mass, and V is the potential difference. Plugging in the values for a proton:

v = sqrt((2×1.60×10^-19 C × 1000 V) / 1.67×10^-27 kg) = 1.84×10^7 m/s

Next, we can use the formula for the radius of a charged particle moving through a magnetic field:

r = mv / (eB)

where B is the magnetic field strength, and we use the velocity we just found. Plugging in the values:

r = (1.67×10^-27 kg × 1.84×10^7 m/s) / (1.60×10^-19 C × 0.040 T) = 0.11 m

Therefore, the answer is B) 0.11 m, as this is the calculated radius of the proton's resulting orbit.

A Proton Starting from Rest Travels Through a Potential of 1.0