A charged particle moves in a region of uniform magnetic field along a helical path (radius = 4.0 cm, pitch = 20 cm, period = 2.0 ms). What is the speed of the particle as it moves along this path?
A) 0.13 km/s
B) 0.10 km/s
C) 0.16 km/s
D) 0.23 km/s
E) 0.06 km/s

Question

Quizplus · Accepted Answer

The speed of a charged particle moving in a magnetic field along a helical path can be calculated using the formula:

v = (2πr / T) * (qB / m)

where:
v = speed of the particle
r = radius of the helix
T = period of the helix
q = charge of the particle
B = strength of the magnetic field
m = mass of the particle

Substituting the given values, we get:

v = (2π * 0.04 m / 0.002 s) * (q * B / m)

We do not have information about the charge and mass of the particle, so we cannot calculate the actual speed. However, we can use the given choices to estimate the answer.

Option C gives the value of v as 0.16 km/s, which is reasonable considering the values of r, T and B. Therefore, the best choice is C.

A Charged Particle Moves in a Region of Uniform Magnetic