Q: (a) Show that / [Hint: Use
(a) Show that / [Hint: Use integration by parts.] (b) Let θ(x) be the step function: Show that dθ/dx = δ(x).
See AnswerQ: (a) Use Eq. 10.75 to calculate the
(a) Use Eq. 10.75 to calculate the electric field a distance d from an infinite straight wire carrying a uniform line charge λ, moving at a constant speed v down the wire. (b) Use Eq. 10.76 to find the m...
See AnswerQ: For the configuration in Prob. 10.15, find the
For the configuration in Prob. 10.15, find the electric and magnetic fields at the center. From your formula for B, determine the magnetic field at the center of a circular loop carrying a steady current...
See AnswerQ: Suppose you take a plastic ring of radius a and glue charge
Suppose you take a plastic ring of radius a and glue charge on it, so that the line charge density is λ0 sin(θ/2) . Then you spin the loop about its axis at an angular veloci...
See AnswerQ: Figure 2.35 summarizes the laws of electrostatics in a “
Figure 2.35 summarizes the laws of electrostatics in a “triangle diagram” relating the source (ρ), the field (E), and the potential (V). Figure 5.48 does the same for magnetostatics, where the source i...
See AnswerQ: An expanding sphere, radius R(t)=vt (t
An expanding sphere, radius R(t)=vt (t > 0, constant v) carries a charge Q, uniformly distributed over its volume. Evaluate the integral with respect to the center. Show that /
See AnswerQ: Check that the potentials of a point charge moving at constant velocity
Check that the potentials of a point charge moving at constant velocity (Eqs. 10.49 and 10.50) satisfy the Lorenz gauge condition (Eq. 10.12).
See AnswerQ: One particle, of charge q1, is held at rest at
One particle, of charge q1, is held at rest at the origin. Another particle, of charge q2, approaches along the x axis, in hyperbolic motion: it reaches the closest point, b, at time t = 0, and then r...
See AnswerQ: We are now in a position to treat the example in Sect
We are now in a position to treat the example in Sect. 8.2.1 quantitatively. Suppose q1 is at x1 =-vt and q2 is at y=-vt (Fig. 8.3, with t < 0). Find the electric and magnetic forces on q1 and q2...
See AnswerQ: (a) Find the fields, and the charge and current
(a) Find the fields, and the charge and current distributions, corresponding to / (b) Use the gauge function / to transform the potentials, and comment on the result.
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