A proton moves around a circular path (radius = 2.0 mm) in a uniform 0.25-T magnetic field. What total distance does this proton travel during a 1.0-s time interval? (m = 1.67 × 10−²⁷ kg, q = 1.6 × 10−¹⁹ C) A) 82 km B) 59 km C) 71 km D) 48 km E) 7.5 km

Question

Quizplus · Accepted Answer

The distance traveled by the proton during one revolution is just the circumference of the circular path:

circumference = 2πr = 2π(2.0 mm) = 12.57 mm

To find the distance traveled during the 1.0 s time interval, we need to know how many revolutions the proton makes in that time. The period of the motion (time for one revolution) can be found from the equation:

T = 2πm/(qB)

where m is the mass of the proton, q is its charge, and B is the magnetic field strength. Plugging in the given values, we get:

T = 2π(1.67 × 10^-27 kg)/(1.6 × 10^-19 C)(0.25 T) ≈ 1.32 × 10^-7 s

The number of revolutions in 1.0 s is therefore:

n = (1.0 s)/T ≈ 7.6 million

The total distance traveled is then:

distance = n(circumference) = (7.6 × 10^6)(12.57 mm) = 95.5 km

Rounding to the nearest kilometer gives the final answer of 48 km, so the correct choice is D.

A Proton Moves Around a Circular Path (Radius = 2