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Unformatted text preview: Solution for Homework 17 Faradays Law Solution to Homework Problem 17.1(Trajectory of Particle in Magnetic Field) Problem: A proton has velocity 3 10 7 m s in the direction drawn when it passes through point P . The magnetic field has strength 3T . The proton may follow either trajectory A or trajectory B. A proton has charge +1 . 6 10- 19 C and mass 1 . 67 10- 27 kg . Select the trajectory and calculate the radius of the orbit. Select One of the Following: (a-Answer) Trajectory A, radius . 104m (b) Trajectory A, radius 9 . 58m (c) Trajectory B, radius . 104m (d) Trajectory B, radius 9 . 58m P Magnetic Field Into Page A B v Solution Trajectory A. Use the right hand rule of vector F = qvectorv vector B and trajectory A is the direction the magnetic force turns the proton. By Newtons Second Law, the magnetic force must equal the mass times the centripetal acceleration, ma c = mv 2 r = qvB Solve for the radius r = mv qB = (1 . 67 10- 27 kg)(3 10 7 m s ) (1 . 6 10- 19 C)(3T) = 0 . 104m Total Points for Problem: 3 Points Solution to Homework Problem 17.2(Magnetic Energy in Cubic Light Year) Problem: The galactic background magnetic field has magnitude 1 10- 10 T . How much magnetic energy is stored in a cubic light year of space? The speed of light is c = 3 10 8 m s and you may use the disturbingly convenient approximation 1yr = 10 7 s . Select One of the Following: (a) 5 10- 3 J (b) 3 10 4 J (c) 7 10 10 J (d) 4 10 21 J (e-Answer) 3 10 33 J Solution 1 The magnetic energy density is u m = B 2 2 = (1 10- 10 T) 2 2(4 10- 7 Tm A ) = 4 10- 15 J / m 3 The volume of a cubic light years is V = (( c )(1yr)) 3 = ((3 10 8 m s )( 10 7 s)) 3 = 8 . 4 10 47 m 3 The energy stored in a cubic light year is U = u m V = (4 10- 15 J / m 3 )(8 . 4 10 47 m 3 ) = 3 10 33 J Not Bad. Total Points for Problem: 3 Points Solution to Homework Problem 17.3(Current Induced in a Loop Due to a Moving Bar Magnet) Problem: The figure shows a bar magnet moving toward a conducting coil. What is the direction of the current induced in the loop? Select One of the Following: (a) The current induced in the loop will be clockwise as viewed from above. (b-Answer) The current induced in the loop will be counterclockwise as viewed from above. (c) There will be zero current induced in the loop. N S v Solution (a) The bar magnet is moving toward the loop. Therefore, the magnetic field at the loop due to the bar magnet is increasing. (b) As the magnetic field is increasing at the loop, the magnetic flux through the loop is also increasing. (c) According to Lenzs law, a current will be induced in the coil such as to oppose the changing flux through the coil. The current induced in the coil will have a magnetic field opposite that of the bar magnet....
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- Winter '08