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Chapter 12: Q11P (page 518)


Short Answer

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01

Expression for the linear speed and the circumference of the circle: 

02

Determine the ratio of the circumference to the diameter:

As the radius stays the same in the inertial frame of reference to another frame of reference, the radius of a circular field does not expand or contract. For considering the circumference, there should be Lorentz-contracted to a smaller value than at rest by a Lorentz factor y. Hence,

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Most popular questions from this chapter

The coordinates of event Aare (xA,0,0),tA, and the coordinates of event B are(xB,0,0),tA. Assuming the displacement between them is spacelike, find the velocity of the system in which they are simultaneous.

An ideal magnetic dipole moment m is located at the origin of an inertial system S¯ that moves with speed v in the x direction with respect to inertial system S. InS¯ the vector potential is

A¯=μ04πm¯×r^¯r¯2

(Eq. 5.85), and the scalar potentialV¯ is zero.

(a) Find the scalar potential V in S.

(b) In the nonrelativistic limit, show that the scalar potential in S is that of an ideal electric dipole of magnitude

p=v×mc2

located atO¯ .

Work out the remaining five parts to Eq. 12.118.

particle’s kinetic energy is ntimes its rest energy, what is its speed?

(a) Repeat Prob. 12.2 (a) using the (incorrect) definition p=mu, but with the (correct) Einstein velocity addition rule. Notice that if momentum (so defined) is conserved in S, it is not conserved inlocalid="1654750932476" S. Assume all motion is along the x axis.

(b) Now do the same using the correct definition,localid="1654750939709" p=mη . Notice that if momentum (so defined) is conserved in S, it is automatically also conserved inlocalid="1654750943454" S. [Hint: Use Eq. 12.43 to transform the proper velocity.] What must you assume about relativistic energy?
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