Questions from Electronics

Q: Suppose J(r) is constant in time, so (

Suppose J(r) is constant in time, so (Prob. 7.60) ρ(r, t) = ρ(r, 0) + ρ˙(r, 0)t . Show that that is, Coulomb’s law holds, with the charge...

Q: Suppose the current density changes slowly enough that we can (to

Suppose the current density changes slowly enough that we can (to good approximation) ignore all higher derivatives in the Taylor expansion J(tr ) = J(t) + (tr − t)J˙(t )...

Q: A particle of charge q moves in a circle of radius a

A particle of charge q moves in a circle of radius a at constant angular velocity ω. (Assume that the circle lies in the xy plane, centered at the origin, and at time t=0 the charge is at (a, 0), on t...

Q: Show that the scalar potential of a point charge moving with constant

Show that the scalar potential of a point charge moving with constant velocity (Eq. 10.49) can be written more simply as / where R= r-vt is the vector from the present (!) position of the particle to...

Q: I showed that at most one point on the particle trajectory communicates

I showed that at most one point on the particle trajectory communicates with r at any given time. In some cases there may be no such point (an observer at r would not see the particle—in the colorful...

Q: Determine the Liénard-Wiechert potentials for a charge in hyperbolic motion

Determine the Liénard-Wiechert potentials for a charge in hyperbolic motion (Eq. 10.52). Assume the point r is on the x axis and to the right of the charge.16

Q: Derive Eq. 10.70. First show that /

Derive Eq. 10.70. First show that

Q: For the configuration in Ex. 10.1, consider a

For the configuration in Ex. 10.1, consider a rectangular box of length l, width w, and height h, situated a distance d above the yz plane (Fig. 10.2). (a) Find the energy in the box at...

Q: Suppose a point charge q is constrained to move along the x

Suppose a point charge q is constrained to move along the x axis. Show that the fields at points on the axis to the right of the charge are given by / (Do not assume v is constant!) What are the fields...

Q: For a point charge moving at constant velocity, calculate the flux

For a point charge moving at constant velocity, calculate the flux integral / (using Eq. 10.75), over the surface of a sphere centered at the present location of the charge.21