Introduction to Electrodynamics 4th. Edition [EXP-2861]

Electrodynamics

Introduction to Electrodynamics 4th. Edition [EXP-2861]

104 SOLVED PROBLEMS

Question: 5.4

(a) A current I is uniformly distributed over a wire of circular cross section, with radius a (Fig. 5.15). Find the volume current density J .

Verified Answer:

The area (perpendicular to the flow) is

\pi ...

Question: 11.2

(a) In the case of an oscillating electric dipole,p(t) = p0 cos(ωt), ¨p(t) = −ω2 p0 cos(ωt),and we recover the results of Sect. 11.1.2.(b) For a single point charge q, the dipole moment is p(t) = qd(t),

Verified Answer:

where d is the position of q with respect to the o...

Question: 3.10

A (physical) electric dipole consists of two equal and opposite charges (±q) separated by a distance d. Find the approximate potential at points far from the dipole.

Verified Answer:

Let η− be the distance from −q and η+ the distance...

Question: 7.1

A cylindrical resistor of cross-sectional area A and length L is made from material with conductivity σ. (See Fig. 7.1; as indicated, the cross section need not be circular, but I do assume it is the same all the way down.) If we stipulate that the potential is constant over each end, and the pot

Verified Answer:

As it turns out, the electric field is uniform wit...

Question: 7.8

A line charge λ is glued onto the rim of a wheel of radius b, which is then suspended horizontally, as shown in Fig. 7.26, so that it is free to rotate (the spokes are made of some nonconducting material—wood, maybe). In the central region, out to radius a, there is a uniform magnetic field B0,

Verified Answer:

The changing magnetic field will induce an electri...

Question: 7.13

A long coaxial cable carries current I (the current flows down the surface of the inner cylinder, radius a, and back along the outer cylinder, radius b) as shown in Fig. 7.40. Find the magnetic energy stored in a section of length l.

Verified Answer:

According to Ampère’s law, the field between the c...

Question: 8.3

A long coaxial cable, of length l, consists of an inner conductor (radius a) and an outer conductor (radius b). It is connected to a battery at one end and a resistor at the other (Fig. 8.5). The inner conductor carries a uniform charge per unit length λ, and a steady current I to the right; the o

Verified Answer:

The fields are

E=\frac{1}{2\pi\epsilon _0}\...

Question: 6.2

A long copper rod of radius R carries a uniformly distributed (free) current I (Fig. 6.19). Find H inside and outside the rod.

Verified Answer:

Copper is weakly diamagnetic, so the dipoles will ...

Question: 2.4

A long cylinder (Fig. 2.21) carries a charge density that is proportional to the distance from the axis: ρ = ks, for some constant k. Find the electric field inside this cylinder.

Verified Answer:

Draw a Gaussian cylinder of length l and radius s....

Question: 7.5

A long cylindrical magnet of length L and radius a carries a uniform magnetization M parallel to its axis. It passes at constant velocity v through a circular wire ring of slightly larger diameter (Fig. 7.22). Graph the emf induced in the ring, as a function of time.

Verified Answer:

The magnetic field is the same as that of a long s...

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