24.4 Sample Problem

To obtain the charge and mass values on the physics datasheet, experimental data was analyzed.  Review samples of such calculations below.

Example Problem 1 
A charged particle is travelling horizontally at 3.60 × 10⁶ m/s through a vertical magnetic field of 0.710 T.  If the radius of the curvature of the particle's path is 0.950 m, what is the charge-to-mass ratio of the particle?

Given

 

Required

the charge-to-mass ratio of the given particle

Analysis and Solution

Paraphrase

The charge-to-mass ratio of the particle is 5.34 × 10⁶ C/kg.

 

Example Problem 2
What is the speed of an electron that passes through an electric field of 6.30 × 10³ N/C and a magnetic field of 7.11 × 10^-3 T undeflected?  The two fields are perpendicular to each other and to the path of the electron.  What is the kinetic energy of the electron?

Given

$$\begin{gathered} \left|\stackrel{\rightharpoonup }{E}\right|=6.30 \times {10}^3 \mathrm{N}/\mathrm{C} \\ \left|\stackrel{\rightharpoonup }{\mathrm{B}}\right|=7.11 \times {10}^{-3} \mathrm{T} \end{gathered}$$

Required

the kinetic energy of the electron

Analysis and Solution

Find the velocity by balancing the force magnetic with the force electric.

Find the kinetic energy.

 

Paraphrase

The kinetic energy of the electron is 3.58 × 10^-19 J.

 

1. An alpha particle travels through a magnetic field of 0.422 T perpendicular to the field.  If the radius of arc of the deflected particle is 1.50 × 10^-3 m, what was the speed of the alpha particle? (3.05 × 10⁴ m/s)

2. A proton travels through a magnetic field at a speed of 5.40 × 10⁵ m/s, perpendicular to the field.  If the radius of curvature is 7.20 mm, what is the magnetic field strength? (0.783 T)

3. Alpha particles travel undeflected through magnetic and electric fields that are perpendicular to each other.  If the speed of the alpha particles was 7.80 × 10⁵ m/s and the magnetic field strength was 0.220 T, what was the electric field strength? (1.72 × 10⁵ N/C)

Watch and Listen Thomson's experiment was about more than just finding the electron; it was also about understanding that matter could be divided into smaller parts.  Watch the video "The Millikan Experiment" until 5:20 to see the glow emitted by a cathode ray tube, Thomson's apparatus, and hear about his work, which effectively demonstrated that the atom was made of divisible parts.

 

  Self-Check

SC 5. Explain how Thomson calculated the unique charge-to-mass ratio for an electron by completing the following statements and equations.

Step 1: Determine the velocity of the electrons by measuring the_______________ and _______________ fields and using this equation:

_________________ 

Step 2: Turn off the _____________ field, leaving only the __________ field, which acts perpendicularly to the velocity of the charged particle. In this orientation the magnetic force causes the charged particle to exhibit ________ motion, giving the following expression for the charge-to-mass ratio:_________________