# hw19 - homework 19 LEE, BENJAMIN Due: Oct 18 2007, 4:00 am...

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homework 19 – LEE, BENJAMIN – Due: Oct 18 2007, 4:00 am 1 Question 1, chap 29, sect 5. part 1 of 1 10 points A cross section of a long solenoid that car- ries current I is shown. I I (into the page) I (out of the page) r All of the following statements about the magnetic Feld v B inside the solenoid are cur- rent EXCEPT 1. The magnitude of b v B b is proportional to the current I . 2. The magnitude of b v B b is proportional to the number of turns of wire per unit length. 3. An approximate value for the magnitude of b v B b may be determined by using Amp` ere’s law. 4. The magnitude of b v B b is proportional to the distance from the axis of the solenoid. correct 5. b v B b is directed to the left. Explanation: ±or the ideal solenoid, b v B b in the inte- rior space is uniform and parallel to the axis and b v B b in the space surrounding the coil is zero. Consider a rectangular path of length and width w , with the sides either parallel or perpendicular to the axis. We can apply Ampere’s law to this path by evaluating the integral of v B · dvs over each side of the rectan- gle, which gives B ℓ = μ 0 N I B = μ 0 n I . It is obvious from the expression above that B is independent of the distance to the axis of the solenoid. Question 2, chap 29, sect 5. part 1 of 1 10 points A point P is at a distance r from the axis of a very tightly wound, inFnitely long solenoid; i.e. , a perfect solenoid. S x y P r z points outward ±ind the magnetic Feld at a point P . 1. B = μ o I 2 π r ˆ z 2. B = μ o n I ˆ x 3. B = μ o I 2 π r ˆ y 4. B = μ o I 2 π r ˆ x 5. B = μ o n I ˆ y 6. B = μ o n I ˆ y 7. B = μ o n I ˆ z 8. B 0 correct 9. B = μ o n I ˆ x 10. B = μ o I 2 π r ˆ x Explanation: The magnetic Feld is contained entirely within the inFnitely-long and tightly wound solenoid. Therefore B 0 . Question 3, chap 29, sect 5. part 1 of 3 10 points The toroid has its inner radius a , its outer

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homework 19 – LEE, BENJAMIN – Due: Oct 18 2007, 4:00 am 2 radius b , a height of h , and its number of turns N . The rectangular cross-sectonal area of the hollow core is ( b a ) h . A r 2 H o llo w C e N t u n s f wi re in id i Find the magnitude of the magnetic ±eld within a toroid at some point P = 1 2 h , where the perpendicular distance from the central axis to the point P is r . 1. B = μ 0 i 2 r 2. B = μ 0 N i 2 π a 3. B = μ 0 i 2 π a 4. B = 0 5. B = μ 0 N i 2 π b 6. B = μ 0 i 2 b 7. B = μ 0 i 2 π b 8. B = μ 0 i 2 π r 9. B = μ 0 N i 2 π r correct 10. B = μ 0 i 2 a Explanation: Basic Concepts: Magnetic Field in Toroid.
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## This note was uploaded on 04/07/2008 for the course PHY 303K taught by Professor Turner during the Fall '07 term at A.T. Still University.

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hw19 - homework 19 LEE, BENJAMIN Due: Oct 18 2007, 4:00 am...

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