Introduction to Electrodynamics - Solution Manuals 4th. Edition by David J. Griffiths | Holooly

Electrodynamics

Introduction to Electrodynamics – Solution Manuals [EXP-2863]

589 SOLVED PROBLEMS

Question: 4.18

The space between the plates of a parallel-plate capacitor (Fig. 4.24) is filled with two slabs of linear dielectric material. Each slab has thickness a, so the total distance between the plates is 2a. Slab 1 has a dielectric constant of 2, and slab 2 has a dielectric constant of 1.5. The free

Verified Answer:

(a) Apply

\int D \cdot d a =Q_{f_{ enc }}...

Question: 8.10

^11 Imagine an iron sphere of radius R that carries a charge Q and a uniform magnetization M = Mzˆ. The sphere is initially at rest. (a) Compute the angular momentum stored in the electromagnetic fields. (b) Suppose the sphere is gradually (and uniformly) demagnetized (perhaps by heating it up p

Verified Answer:

(a)

E =\left\{\begin{array}{ll} 0 , & (...

Question: 8.13

^16 A very long solenoid of radius a, with n turns per unit length, carries a current Is. Coaxial with the solenoid, at radius b ≪ a, is a circular ring of wire, with resistance R. When the current in the solenoid is (gradually) decreased, a current Ir is induced in the ring. (a) Calculate Ir, in

Verified Answer:

\text { (a) } ε =-\frac{d \Phi}{d t} ; \Phi...

Question: 8.16

^17 A sphere of radius R carries a uniform polarization P and a uniform magnetization M (not necessarily in the same direction). Find the electromagnetic momentum of this configuration. [Answer: (4/9)πμ0R^3(M × P)]

Verified Answer:

According to Eqs. 3.104, 4.14, 5.89, and 6.16, the...

Question: 8.17

^18 Picture the electron as a uniformly charged spherical shell, with charge e and radius R, spinning at angular velocity ω. (a) Calculate the total energy contained in the electromagnetic fields. (b) Calculate the total angular momentum contained in the fields. (c) According to the Einstein

Verified Answer:

(a) From Eq. 5.70 and Prob. 5.37,

B = \nabl...

Question: 11.21

^19 An electric dipole rotates at constant angular velocity ω in the xy plane. (The charges, ±q, are at r± = ±R(cos ωt xˆ + sin ωt yˆ); the magnitude of the dipole moment is p = 2q R.) (a) Find the interaction term in the self-torque (analogous to Eq. 11.99). Assume the motion is nonrelativistic

Verified Answer:

(a) The total torque is twice the torque on +q; we...

Question: 10.32

^22 A particle of charge q1 is at rest at the origin. A second particle, of charge q2, moves along the z axis at constant velocity v. (a) Find the force F12(t) of q1 on q2, at time t (when q2 is at z = vt). (b) Find the force F21(t) of q2 on q1, at time t. Does Newton’s third law hold, in this

Verified Answer:

\text { (a) } F _{12}(t)=\frac{1}{4 \pi \ep...

Question: 12.68

“Derive” the Lorentz force law, as follows: Let charge q be at rest in S¯, so F¯ = qE¯ , and let S¯ move with velocity v = υ xˆ with respect to S. Use the transformation rules (Eqs. 12.67 and 12.109) to rewrite F¯ in terms of F, and E¯ in terms of E and B. From these, deduce the formula for F

Verified Answer:

Equation 12.67 assumes the particle is (instantane...

Question: 3.55

(a) A long metal pipe of square cross-section (side a) is grounded on three sides, while the fourth (which is insulated from the rest) is maintained at constant potential V0. Find the net charge per unit length on the side opposite to V0. [Hint: Use your answer to Prob. 3.15 or Prob. 3.54.]

Verified Answer:

(a) Using Prob. 3.15b (with b = a):

V(x, y)...

Question: 11.17

(a) A particle of charge q moves in a circle of radius R at a constant speed υ. To sustain the motion, you must, of course, provide a centripetal force mυ2/R; what additional force (Fe) must you exert, in order to counteract the radiation reaction? [It’s easiest to express the answer in t

Verified Answer:

(a) To counteract the radiation reaction (Eq. 11.8...

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