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# xHW9 - Version One – Homework 9 – Savrasov – 39821...

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Unformatted text preview: Version One – Homework 9 – Savrasov – 39821 – May 14, 2007 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Induced EMF for a Wire Loop 31:01, calculus, numeric, > 1 min, normal. 001 (part 1 of 4) 1 points The circular loop of wire shown in the figure is placed in a spatially uniform magnetic field such that the plane of the circular loop is per- pendicular to the direction for the magnetic field as shown in the figure. The magnetic field ~ B ( t ) varies with time, with the time de- pendence given by B ( t ) = a + b t , where a = 0 . 13 T and b = 0 . 017 T / s. The acceleration due to gravity is 9 . 8 m / s 2 . r = 2 . 2 cm radius B ( t ) What is the magnetic flux through the loop as a function of time? 1. Φ B ( t ) = 2 a π r 2. Φ B ( t ) = b π r 2 3. Φ B ( t ) = a π r 2 4. Φ B ( t ) = ( a + b ) π r 2 5. Φ B ( t ) = ‡ a t + b · π r 2 6. Φ B ( t ) = 2 b π r 7. Φ B ( t ) = ( a + b t ) π r 2 correct 8. Φ B ( t ) = 2( a + b ) π r 9. Φ B ( t ) = 2 ‡ a t + b · π r 10. Φ B ( t ) = 2( a + b t ) π r Explanation: Faraday’s Law of Induction E ind =- d Φ B dt =- ΔΦ B Δ t . Lenz’ Law is used to find direction of E ind . Magnetic flux is defined by Φ B ≡ Z S ~ B · d ~ A = ~ B · ~ A . The definition of resistance is R ≡ ρ L A . Power dissipated in a resistor is P = I V = I 2 R = V 2 R . In this case, B ( t ) is uniform over the surface defined by the wire loop and perpendicular to this surface, so the magnetic flux simplifies to Φ B ( t ) = B ( t ) A = B ( t ) π r 2 . Substituting the value of B at time, t , we find that Φ B ( t ) = ( a + b t ) π r 2 . See the results of oppose the increase in the magnetic flux, the magnetic field generated by the induced current must be in the opposite direction as the original magnetic field. Using the right-hand rule, we see that this is in the clockwise direction. Since the current must be in the same direction as the E , the E...
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xHW9 - Version One – Homework 9 – Savrasov – 39821...

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