A student models an electron executing uniform circular motion around a single…
PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism
Problem
A student models an electron executing uniform circular motion around a single isolated proton. She records the orbital radius r and the speed v predicted by classical mechanics for four different hypothetical orbits. Her results are summarized in the table below.
Radius r (10−10m)
Speed v (106ms−1)
0.50
4.4
1.0
3.1
2.0
2.2
4.0
1.6
All measurements are reported to two significant figures.
(a) Describe the qualitative trend shown by the data in the table. Include a statement about how the orbital speed changes as the radius increases.
(b) Explain, using fundamental principles of mechanics and electrostatics, why the speed of the electron is expected to vary in proportion to r−1/2. Your explanation should explicitly connect the required radial acceleration for circular motion to the interaction between the charges.
(c) State two key assumptions inherent in using this classical model to predict the electron’s motion. For each assumption, briefly justify why it is necessary for the analysis.