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Chapter 28: Q23P (page 830)
What uniform magnetic field, applied perpendicular to a beam of electrons moving at m/s, is required to make the electrons travel in a circular arc of radius 0.350 m?
The required magnetic field is .
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In Figure, a metal wire of mass m = 24.1 mg can slide with negligible friction on two horizontal parallel rails separated by distance d = 2.56 cm. The track lies in a vertical uniform magnetic field of magnitude 56.3 mT. At time t = 0, device Gis connected to the rails, producing a constant current i = 9.13 mA in the wire and rails (even as the wire moves). Att = 61.1 ms, (a) what is the wire’s speed? (b) What is the wire’s direction of motion (left or right)?
A wire of length 25.0cm carrying a current of 4.51mAis to be formed into a circular coil and placed in a uniform magnetic fieldof magnitude 5.71mT. If the torque on the coil from the field is maximized. What are (a) the angle between and the coil’s magnetic dipole moment? (b) the number of turns in the coil? (c) What is the magnitude of that maximum torque?
(a) In Fig. 28-8, show that the ratio of the Hall electric field magnitude E to the magnitude Ecof the electric field responsible for moving charge (the current) along the length of the strip is
where is the resistivity of the material and nis the number density of the charge carriers. (b) Compute this ratio numerically for Problem 13. (See Table 26-1.)
An alpha particle can be produced in certain radioactive decays of nuclei and consists of two protons and two neutrons. The particle has a charge of and a mass of , where is the atomic mass unit, with kg. Suppose an alpha particle travels in a circular path of radius cm in a uniform magnetic field with . Calculate (a) its speed (b) its period of revolution, (c) its kinetic energy, and (d)the potential difference through which it would have to be accelerated to achieve this energy.
A proton circulates in a cyclotron, beginning approximately at rest at the center. Whenever it passes through the gap between Dees, the electric potential difference between the Dees is 200 V.
(a)By how much does its kinetic energy increase with each passage through the gap?
(b)What is its kinetic energy as it completes 100passes through the gap? Let r100be the radius of the proton’s circular path as it completes those 100passes and enters a dee, and let r101be its next radius, as it enters a dee the next time.
(c)By what percentage does the radius increase when it changes from r100to r101? That is, what is Percentage increase =?
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