Q11P ... [FREE SOLUTION]

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Introduction to Electrodynamics

David J. Griffiths

Physics

4th edition Edition · 613 pages

ISBN: 9780321856562

Chapter 12: Q11P (page 518)

Short Answer

Expert verified

Step by step solution

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

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

Solve Eqs. 12.18 for $x, y, z, t$ in terms of $x, y, z, t$ and check that you recover Eqs. 12.19.

Suppose you have a collection of particles, all moving in the x direction, with energies $E_{1}, E_{2}, E_{3, . . . . . . . . . . . .}$ . and momenta $p_{1}, p_{2}, p_{3, . . . . . . . . . . . . . . .}$ . Find the velocity of the center of momentum frame, in which the total momentum is zero.

An ideal magnetic dipole moment m is located at the origin of an inertial system $\bar{S}$ that moves with speed v in the x direction with respect to inertial system S. In $\bar{S}$ the vector potential is

$\bar{A} = \frac{μ_{0}}{4 π} \frac{\bar{m} \times \bar{\hat{r}}}{{\bar{r}}^{2}}$

(Eq. 5.85), and the scalar potential $\bar{V}$ 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

$p = \frac{v \times m}{c^{2}}$

located at $\bar{O}$ .

Show that the (ordinary) acceleration of a particle of mass m and charge q, moving at velocity u under the influence of electromagnetic fields E and B, is given by

$a = \frac{q}{m} \sqrt{1 ‐ u^{2} / c^{2}} [E + u \times B - \frac{1}{c^{2}} u (u ‐ E)]$

[Hint: Use Eq. 12.74.]

(a) Equation 12.40 defines proper velocity in terms of ordinary velocity. Invert that equation to get the formula for u in terms of $η$ .

(b) What is the relation between proper velocity and rapidity (Eq. 12.34)? Assume the velocity is along the x direction, and find as a function of $θ$ .

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Short Answer

Step by step solution

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

Determine the ratio of the circumference to the diameter:

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Most popular questions from this chapter

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