Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 20 - Magnetism - Problems - Page 584: 16

Answer

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Work Step by Step

a. Use the relationship from Example 20-6, page 567. $$r=\frac{mv}{qB} $$ Solve for the speed. $$v=\frac{rqB}{m} $$ Now write an expression for the KE. $$KE=\frac{1}{2}mv^2=\frac{1}{2}m(\frac{rqB}{m})^2=\frac{r^2q^2B^2}{2m}$$ The kinetic energy is proportional to the square of the radius of curvature, which was to be shown. b. For a particle moving in a circular path, the angular momentum is L=mvr. Use the relationship from Example 20-6, page 567. $$r=\frac{mv}{qB} $$ Solve for the speed. $$v=\frac{rqB}{m} $$ Now write an expression for the angular momentum. $$L=mvr=m(\frac{rqB}{m})r=qBr^2$$ This was to be shown.
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