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Magnetic field due to current in a straight wire A long,

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 82 Chapter 7.4

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 82

Magnetic field due to current in a straight wire A long, straight wire of length 2L on the y-axis carries a current I. According to the Biot-Savart Law, the magnitude of the magnetic field due to the current at a point 1a, 02 is given by B1a2 = m0 I 4p L L -L sin u r2 dy, where m0 is a physical constant, a 7 0, and u, r, and y are related as shown in the figure. a. Show that the magnitude of the magnetic field at 1a, 02 is B1a2 = m0 IL 2p a2a2 + L2 . b. What is the magnitude of the magnetic field at 1a, 02 due to an infinitely long wire 1LS _2?

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CLA Monsters 3/3/2016 Scylla (Skylla) cont’d (Scylla as depicted in Greek world, in this case on a coin) She’s important because she’s a midway between the hydra, chimera, and Hesiod echidna because of her impregnability o The Scylla you get in Homer doesn’t occur by herself, she comes as a pair with Charybdis o Possible to escape from her, unlike Echidna, though you will lose some men How do these two monsters work as a pair o Look at sourcebook under Scylla o There is a later source that talks about how Heracles killed Scylla Back to her in the Odyssey:  Typical iconography is not contradictory to her Homeric description Obvious differences:  DESCRIPTION IN HOMER:  12 feet  6 very long necks  1 head at the end of each very long neck Dogs o Under her skirt, where her virginity is kept o Upper half looks like a non-frightening young girl  Like the Sirens o Not the type of maiden to be tamed by marriage The Scylla (and the Sirens) are to be understood as young maidens who can’t be bound by marriage. They have escaped the domestication of marriage; they live in total isolation o This idea is what has been plaguing Odysseus, who only meets these creatures because Circe told him too. Can she really be trusted o Remember she lured Odysseus with the illusion of domestication, and sends him to women who are the complete opposite THINK: What makes them monstrous is that they do not operate under the framework of marriage: they are maidens on the loose Compare the danger of Scylla and the Cyclopes:  They live far removed from normal society, in caves  They live on their own versions of islands  As far as Odysseus is concerned in confronting them: he has to outsmart the Cyclops, but his metis is completely useless when it comes to Scylla o She is far beyond his league, the odds against Scylla if you are Odysseus is 0%, and we have never seen such odds before Now back to the dogs:  Puppy sounds o In other sources it says that the sounds aren’t coming from her but her victims, when she grabs them and eats them. o In a sense she only really exists (as in making noise) when she is eating her victim Explaining the 12 feet:  If we can’t see her bottom half, where are her feet o There are two feet at the base of her head o The feet belong to her victims, as in her mouths at the end of very long necks (or tentacles) o If these are not a permanent figure, that means that she is constantly attacking some 6 sailors somewhere The only choice is to get closer to her than Charybdis Scylla’s Iconographical depiction (compared to Homer)  Top half, human girl  Lower half is shown, while in Homer it is hidden o Artists are forced to be detailed in her representation o In homer her top half, is an extension if what her lower half must be like—a big mouth with teeth But what matters is the devouring mouths at her top, for Homer Lead us to her counterpart Charybdis: There is no Scylla without Charybdis, Why not  Charybdis’ crag is much lower and she doesn’t dwell inher cliff, but she flows around it  She is a whirlpool, remember  Why the cliff is he doesn’t live in it o Her boundary marker, the cliff is her center o Remember Scylla’s cliff is turned towards the underworld, west and is associated with the underworld, but Charybdis’ has a “great” fig tree full of leaves, it living and thriving in this weird situation (in the middle of the sea) (Fig Tree) Back to Odysseus:  Follows directions and loses his 6 men  They leave the strait of the two monsters and go to the island of Helios (where they eat his cows, which they were not earned to do)  They get on the ship, get shipwrecked by the thunderbolt of Zeus, with Odysseus is the only one surviving…then we return to Charybdis “Then verily the West Wind ceased to blow tempestuously, and swiftly the South Wind came, bringing sorrow to my heart, that I might traverse again the way to baneful Charybdis. All night long was I borne, and at the rising of the sun [430] I came to the cliff of Scylla and to dread Charybdis. She verily sucked down the salt water of the sea, but I, springing up to the tall fig-tree, laid hold of him, and clung to it like a bat. Yet I could in no wise plant my feet firmly or climb upon the tree, [435] for its roots spread far below and its branches hung out of reach above, long and great, and overshadowed Charybdis. There I clung steadfastly until she should vomit forth mast and keel again, and to my joy they came at length. At the hour when a man rises from the assembly for his supper, [440] one that decides the many quarrels of young men that seek judgment, even at that hour those spars appeared from out Charybdis. And I let go hands and feet from above and plunged down into the waters out beyond the long spars, and sitting on these I rowed onward with my hands. [445] But as for Scylla, the father of gods and men did not suffer her again to catch sight of me, else should I never have escaped utter destruction.”  He drifts back to that straight again, but directly to Charybdis, right at the moment she is sucking down water  Odysseus is clinging to the Fig tree, hanging on the trunk like a bat o The roots and branches were two low/high to reach, and the branches were so large they overshadowed the whirlpool o She sucks you in and spits you out (she doesn’t eat you “[445] But as for Scylla, the father of gods and men did not suffer her again to catch sight of me, else should I never have escaped utter destruction.”  Zeus o No god could help him before Why does Zeus intervene in this instance, and only in this instance  Keep this question in mind THINK: What do you make of the fact that Odysseus is brought back to this strait o KEEP IN MIND: He was willing to sacrifice six men to avoid Charybdis, keep in mind the fig tree at her center o The Fig tree is life or hope: The abundance of nature o Charybdis is raw, untamed nature, that Zeus or the Olympians never controlled  Which is why Circe says Poseidon can’t even help  Now Odysseus is like a regular sailor, pitted against the sea (nature) from now on  Because of this, you can describe Odysseus as a new kind of Hero who has r brave this new monster (untamed nature), one explanation he is drawn back to her instead of Scylla (who is a representative of the old type of monster) THINK: If she is this new kind of monster, why is she female  Who caused the end of the golden age o Pandora. Now men have to deal with problems they no longer had, before this woman o Man has to now be a survivor, which is what Odysseus is (he has to be adaptive, patient) Back to the interaction of Zeus: “[445] But as for Scylla, the father of gods and men did not suffer her again to catch sight of me, else should I never have escaped utter destruction.”  Why now o It’s like saying the times are changing, Scylla is an outdated paradigm, she is not a working model with the new force of the untamable sea o New kind of Hero, new kind of monster o Think of his epithets: long enduring and Polytropos  One who can turn in many directions, or is ever resourceful, which comes in handy when dealing with these new monsters Other reasons Odysseus has to confront Charybdis—all on his own:  He can’t even escape, he survives because she chooses to help him by aid of her fig tree  But Zeus has no power over them Different from Leviathan and the Behemoth: Christian God, creates and can control them

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Chapter 7.4, Problem 82 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

The full step-by-step solution to problem: 82 from chapter: 7.4 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. The answer to “Magnetic field due to current in a straight wire A long, straight wire of length 2L on the y-axis carries a current I. According to the Biot-Savart Law, the magnitude of the magnetic field due to the current at a point 1a, 02 is given by B1a2 = m0 I 4p L L -L sin u r2 dy, where m0 is a physical constant, a 7 0, and u, r, and y are related as shown in the figure. a. Show that the magnitude of the magnetic field at 1a, 02 is B1a2 = m0 IL 2p a2a2 + L2 . b. What is the magnitude of the magnetic field at 1a, 02 due to an infinitely long wire 1LS _2?” is broken down into a number of easy to follow steps, and 121 words. Since the solution to 82 from 7.4 chapter was answered, more than 234 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.

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