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1C_Fall2008_MT1sols

# 1C_Fall2008_MT1sols - Midterm 1 – Fall 2008 SOLUTIONS...

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Unformatted text preview: Midterm 1 – Fall 2008 SOLUTIONS Physics 1C, R. Richard Tuesday, October 21 Please do the 4 following problems. Show all work and reasoning. Use the back of the page if necessary and circle your final answer. Write your name and student ID on your exam. Problem # Score 1 2 3 4 Total Selected Formulas and Constants Permittivity of Free Space 2 2 12 m N / C 10 85 . 8 ⋅ × = − ε 2 2 9 C / m N 10 99 . 8 4 / 1 ⋅ × = πε Permeability of free space m/A T 10 4 7 ⋅ × = − π μ Integrals ) 1 ( 1 1 − ≠ + = + ∫ n n x dx x n n ax a axdx sin 1 cos ∫ = ax a axdx cos 1 sin ∫ − = ∫ = x x dx ln Rotation and linear speed v = r ω Capacitor Stored Energy U=Q 2 /2C Mechanical Power P=Fv (translational) P = τω (rotational) Problem 1 The Faraday disk dynamo consists of a rotating, conducting disk on an axle, as shown below. The disk has a radius R = 21.0 cm and it rotates counterclockwise at a rate of 580.00 radians per second. It is immersed in a uniform magnetic field of 0.400 T directed perpendicular to the disk surface. A 24.0 Ω resistor R is located on a wire between the axle and the rim. Sliding connections allow the wire to connect to the rotating disk and axle. The current direction shown is arbitrary; the current may actually flow in the opposite direction. (10 pts.) a) What is the magnitude of the emf induced between the center and the rim of the disk? The rotation of the disk induces a motional emf. Because the velocity of a point on the disk varies with radial distance, you must integrate from the center to the rim of the disk. The velocity and magnetic field vectors are perpendicular. and magnetic field vectors are perpendicular....
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1C_Fall2008_MT1sols - Midterm 1 – Fall 2008 SOLUTIONS...

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