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Chapter 7: Q7.38P (page 348)
Question: Assuming that "Coulomb's law" for magnetic charges ( qm) reads
Work out the force law for a monopole moving with velocity through electric and magnetic fields E and B.
Answer
The value of the magnetic charge is
.
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An alternating current I(t) (amplitude 0.5 A, frequency ) flows down a straight wire, which runs along the axis of a toroidal coil with rectangular cross section (inner radius 1cm , outer radius 2 cm , height 1 cm, 1000 turns). The coil is connected to a 500 resistor.
(a) In the quasistatic approximation, what emf is induced in the toroid? Find the current, , in the resistor.
(b) Calculate the back emf in the coil, due to the current . What is the ratio of the amplitudes of this back emf and the "direct" emf in (a)?
Question:Calculate the energy stored in the toroidal coil of Ex. 7.11, by applying Eq. 7.35. Use the answer to check Eq. 7.28.
A rectangular loop of wire is situated so that one end (height h) is between the plates of a parallel-plate capacitor (Fig. 7.9), oriented parallel to the field E. The other end is way outside, where the field is essentially zero. What is the emf in this loop? If the total resistance is R, what current flows? Explain. [Warning: This is a trick question, so be careful; if you have invented a perpetual motion machine, there's probably something wrong with it.]
In the discussion of motional emf (Sect. 7.1.3) assumed that the wire loop (Fig. 7.10) has a resistance ; the current generated is then . But what if the wire is made out of perfectly conducting material, so that is zero? In that case, the current is limited only by the back emf associated with the self-inductance of the loop (which would ordinarily be negligible in comparison with ). Show that in this regime the loop (mass ) executes simple harmonic motion, and find its frequency. [Answer: ].
A small loop of wire (radius a) is held a distance z above the center of a large loop (radius b ), as shown in Fig. 7.37. The planes of the two loops are parallel, and perpendicular to the common axis.
(a) Suppose current I flows in the big loop. Find the flux through the little loop. (The little loop is so small that you may consider the field of the big loop to be essentially constant.)
(b) Suppose current I flows in the little loop. Find the flux through the big loop. (The little loop is so small that you may treat it as a magnetic dipole.)
(c) Find the mutual inductances, and confirm that ·
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