# 19 - Kapoor(mk9499 – oldhomework 19 – Turner –(60230...

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Unformatted text preview: Kapoor (mk9499) – oldhomework 19 – Turner – (60230) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A cross section of a long solenoid that carries current I is shown. I I (into the page) I (out of the page) r All of the following statements about the magnetic field vector B inside the solenoid are cur- rent EXCEPT 1. The magnitude of bardbl vector B bardbl is proportional to the number of turns of wire per unit length. 2. An approximate value for the magnitude of bardbl vector B bardbl may be determined by using Amp` ere’s law. 3. bardbl vector B bardbl is directed to the left. 4. The magnitude of bardbl vector B bardbl is proportional to the distance from the axis of the solenoid. correct 5. The magnitude of bardbl vector B bardbl is proportional to the current I . Explanation: For the ideal solenoid, bardbl vector B bardbl in the inte- rior space is uniform and parallel to the axis and bardbl vector B bardbl in the space surrounding the coil is zero. Consider a rectangular path of length ℓ 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 vector B · dvectors over each side of the rectan- gle, which gives B ℓ = μ N I B = μ n I . It is obvious from the expression above that B is independent of the distance to the axis of the solenoid. 002 10.0 points A point P is at a distance r from the axis of a very tightly wound, infinitely long solenoid; i.e. , a perfect solenoid. S x y P r z points outward Find the magnetic field at a point P . 1. B = μ o I 2 π r ˆ y 2. B ≈ correct 3. B = − μ o n I ˆ x 4. B = μ o n I ˆ x 5. B = μ o n I ˆ z 6. B = − μ o I 2 π r ˆ x 7. B = − μ o I 2 π r ˆ z 8. B = μ o n I ˆ y 9. B = μ o I 2 π r ˆ x 10. B = − μ o n I ˆ y Explanation: The magnetic field is contained entirely within the infinitely-long and tightly wound solenoid. Therefore B ≈ . 003 (part 1 of 3) 10.0 points The toroid has its inner radius a , its outer radius b , a height of h , and its number of Kapoor (mk9499) – oldhomework 19 – Turner – (60230) 2 turns N . The rectangular cross-sectonal area of the hollow core is ( b − a ) h . A r 2 r h o llo w c o r e N t u r n s o f wi re in t o r o i d i Find the magnitude of the magnetic field within a toroid at some point P = 1 2 h , where the perpendicular distance from the central axis to the point P is r ....
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19 - Kapoor(mk9499 – oldhomework 19 – Turner –(60230...

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