gence of curl is zero? Show that Ampère's law cannot be valid, in general, outside mag- netostatics. Is there any such "defect" in the other three of Maxwell's equations? Problem 5.24 Suppose there did exist magnetic monopoles. How would you modify Max- well's equations (for electro/magnetostatics) and the Lorentz force law to accommodate them? If you think there are several plausible options, list them, and suggest how you might determine experimentally which one is right.

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Please write Problem 5.24
Problem 5.22
(a) Find the density p of mobile charges in a piece of copper, assuming each atom con
tributes two free electrons.
(b) Calculate the average electron velocity in a copper wire 1 mm in diameter which
carries a current of 1 A. (Note: this is literally a snail's pace. How, then, can you carry
on a long distance telephone conversation?)
(c) What is the force of attraction between two such wires, 1 cm apart?
(d) If you could somehow remove the stationary positive ions, what would the electrical
repulsion force be? How many times greater than the magnetic force is it?
Problem 5.23 Is Ampère's law consistent with the general rule (equation (1.37)) that diver-
gence of curl is zero? Show that Ampère's law cannot be valid, in general, outside mag-
netostatics. Is there any such "defect" in the other three of Maxwell's equations?
Problem 5.24 Suppose there did exist magnetic monopoles. How would you modify Max-
well's equations (for electro/magnetostatics) and the Lorentz force law to accommodate
them? If you think there are several plausible options, list them, and
might determine experimentally which one is right.
suggest how
ENETIC VECTOR POTENTIAL
4.1 The Vector Potential
st as V XE = 0 permitted us to introduce a scalar potential
E=-VV
you
ostatics,
Transcribed Image Text:Problem 5.22 (a) Find the density p of mobile charges in a piece of copper, assuming each atom con tributes two free electrons. (b) Calculate the average electron velocity in a copper wire 1 mm in diameter which carries a current of 1 A. (Note: this is literally a snail's pace. How, then, can you carry on a long distance telephone conversation?) (c) What is the force of attraction between two such wires, 1 cm apart? (d) If you could somehow remove the stationary positive ions, what would the electrical repulsion force be? How many times greater than the magnetic force is it? Problem 5.23 Is Ampère's law consistent with the general rule (equation (1.37)) that diver- gence of curl is zero? Show that Ampère's law cannot be valid, in general, outside mag- netostatics. Is there any such "defect" in the other three of Maxwell's equations? Problem 5.24 Suppose there did exist magnetic monopoles. How would you modify Max- well's equations (for electro/magnetostatics) and the Lorentz force law to accommodate them? If you think there are several plausible options, list them, and might determine experimentally which one is right. suggest how ENETIC VECTOR POTENTIAL 4.1 The Vector Potential st as V XE = 0 permitted us to introduce a scalar potential E=-VV you ostatics,
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