EBK COLLEGE PHYSICS
2nd Edition
ISBN: 9780134605500
Author: ETKINA
Publisher: PEARSON CO
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Textbook Question
Chapter 30, Problem 6P
Use Newtonian circular motion concepts to show that the radius r of the circle in which a charged particle spirals while moving perpendicular to a magnetic field is proportional to the particle’s speed V.
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Consider a region where the electric field and the magnetic field are along the +x- and the -y-axes, respectively.
If a certain charge is in the region, at what velocity should it move so that it will move in a uniform velocity? (To
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and of the magnetic field, respectively.
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AI answered the problem this way. Is this correct?
The Lorentz force that makes a charged particle move in a circular path in a magnetic field is given by
F=qvBF=qvB
where qq is the charge of the particle, vv is the speed of the particle, and BB is the magnetic field strength.
Since the particle is moving in a circular path, this force must equal the centripetal force, F=mv2rF=rmv2, where mm is the mass of the particle and rr is the radius of the circular path.
Setting the two expressions for FF equal to each other, we get
qvB=mv2rqvB=rmv2
Since we want to find the frequency of the orbit, we need to find the speed vv of the proton. Given that the energy of the proton is 1 MeV, we can write
12mv2=1 MeV21mv2=1MeV
and solve for vv:
v=2×1 MeVmv=m2×1MeV
where mm is the mass of a proton, which is approximately 1.67×10−27 kg1.67×10−27kg.
Substituting this expression for vv into the expression for the Lorentz force, we can solve for the frequency of the orbit. The frequency is related to…
The Schwarzschild radius RBH for an object of mass M is defined as
(See image.)
where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole.
1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass?
2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass?
3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?
Chapter 30 Solutions
EBK COLLEGE PHYSICS
Ch. 30 - Prob. 1RQCh. 30 - Prob. 2RQCh. 30 - Review Question 30.3 Using what you have learned...Ch. 30 - Prob. 4RQCh. 30 - Prob. 5RQCh. 30 - Prob. 1MCQCh. 30 - Prob. 2MCQCh. 30 - Prob. 3MCQCh. 30 - Prob. 4MCQCh. 30 - Prob. 5CQ
Ch. 30 - Prob. 6CQCh. 30 - Prob. 7CQCh. 30 - Prob. 8CQCh. 30 - Prob. 9CQCh. 30 - Prob. 10CQCh. 30 - Prob. 11CQCh. 30 - 12. What are the components of the Standard...Ch. 30 - Prob. 13CQCh. 30 - Prob. 14CQCh. 30 - Prob. 1PCh. 30 - Prob. 2PCh. 30 - Prob. 3PCh. 30 - Prob. 4PCh. 30 - Prob. 5PCh. 30 - 6. Use Newtonian circular motion concepts to show...Ch. 30 - Prob. 7PCh. 30 - A particle enters a cloud chamber from above...Ch. 30 - Prob. 9PCh. 30 - Prob. 10PCh. 30 - Prob. 11PCh. 30 - Prob. 12PCh. 30 - Prob. 13PCh. 30 - 14. * Make an analogy between the interactions of...Ch. 30 - Why are neutrinos difficult to detect?Ch. 30 - Prob. 16PCh. 30 - Prob. 17PCh. 30 - Prob. 18PCh. 30 - Prob. 19PCh. 30 - Prob. 20PCh. 30 - Prob. 21PCh. 30 - Prob. 22PCh. 30 - Prob. 23PCh. 30 - Prob. 24PCh. 30 - Prob. 25PCh. 30 - Prob. 26PCh. 30 - * What is inflation, and what eventually happened...Ch. 30 - Prob. 29PCh. 30 - Prob. 30PCh. 30 - Prob. 31PCh. 30 - * Our bodies contain significant amounts of...Ch. 30 - 33. * What is the evidence that a large proportion...Ch. 30 - Prob. 34PCh. 30 - 35. * What is the experimental evidence for dark...Ch. 30 - Prob. 36PCh. 30 - Prob. 37PCh. 30 - Prob. 38PCh. 30 - Prob. 39PCh. 30 - * An electron and a positron are traveling...Ch. 30 - Prob. 41GPCh. 30 - Prob. 42RPPCh. 30 - Prob. 43RPPCh. 30 - Prob. 44RPP
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