St. Vincent College PH 112-01: General Physics II Exam 5 4/8/2016 The exam consists of 4 questions. The questions may not be worth the same number of points, so read the entire exam before beginning work. You must show your work in order to get full credit. Problem 1 20 Problem 2 30 Problem 3 20 Problem 4 30 Total 100 v f = v i + at x f x i = v i t + (1/2)at 2 x f x i = (1/2)(v i + v f )t v 2 f = v2 i + 2a(x f x i ) E = cb v = fλ E = hf n = c/v n i p + n t q = n t n i R M = n iq n t p g = 9.8 m/s 2 down 1 inch = 2.54 cm (exact) 1 mile = 5280 feet 1 J = 6.24 10 18 ev 1 lb = 4.448 N 746 W = 1 hp k e = 8.99 10 9 N m 2 /C 2 ǫ 0 = 8.85 10 12 C 2 /N m 2 µ 0 = 4π 10 7 T m/a e = 1.6 10 19 C Electron m e = 9.11 10 31 kg Proton m p = 1.67 10 27 kg Neutron m n = 1.67 10 27 kg c = 3 10 8 m/s G = 6.67 10 11 N m 2 /kg 2 Solid Cylinder or Disc I = (1/2)MR 2 Hollow Cylinder or Hoop I = MR 2 Solid Sphere I = (2/5)MR 2 Spherical Shell I = (2/3)MR 2 Rod about one end I = (1/3)ML 2 Rod about center I = (1/12)ML 2 Radius of Earth r E = 6.38 10 6 m Mass of Earth m E = 5.98 10 24 kg
1. (20 pts) a) (5 pts) Which would be more effective in changing the inductance of a solenoid: doubling the current through it or stretching the ends so that the length doubles? Explain. b) (5 pts) Which would be more dangerous to a person wearing a conductive bracelet: a region of space with a very large but constant magnetic field, or a region of space with a small magnetic field that is changing very rapidly. Why? c) (5 pts) If you want the current in a particular circuit to reach its final maximum value sooner, should you try to increase or decrease the self-inductance of the circuit? d) (5 pts) In the Latrobe area, the Earth s magnetic field points generally to the north. If you were to hold a long metal pole horizontally while facing north [so that one end is to your left (west) and the other end is to your right (east)], in what direction would you need to move the pole in order to make the right end positively charged?
2. (30 pts) A sliding bar, shown below, has a length of 0.5 m and moves with a velocity of 2 m/s to the left through a magnetic field of 0.25 T that is pointing into the page. The resistance between the two frictionless conducting rails along which the bar slides is 0.5 Ω. l R v a) (15 pts) Work out the induced potential between the ends of the sliding rod and the amount of current that subsequently flows through the resistor. There is more than one way to do this, use whichever way with which you feel most comfortable. (Or whichever way you happen to remember.) b) (5 pts) Determine the direction in which the induced current flows in this situation. It is probably easiest to draw your response right on the figure above. c) (10 pts) How much force would need to be applied to the sliding rod, and in what direction, to keep it moving at a constant 2 m/s through the magnetic field?
3. (20 pts) Determine the direction of the induced current indicated in each of the situations shown below. If you include the argument you used to work out the direction, partial credit may be possible in the event your final answer is incorrect. N + S Determine the current induced in the conducting ring as it falls away from the magnet. Determine the direction of induced current in the resistor just after the switch has been closed (i.e. just after the circuit has been turned on). I If the current in thicker, long wire is decreasing, determine the direction of the current induced in rectangular loop. The square loop is not moving, but a magnetic field is pointing out of the page and getting larger in magnitude. Determine the direction of the current induced in the square loop.
4. (30 pts) A circular coil enclosing an area of 100 cm 2 is made of 200 turns of copper wire. The wire used to make the coil has a resistance of 5 Ω. The ends of the wire are connected so as to make a closed circuit. Initially, a 1.1 T uniform magnetic field points perpendicularly upward through the (horizontal) plane of the coil. The direction of the magnetic field then reverses so that the final magnetic field has a magnitude of 1.1 T pointing downward, perpendicular to the (still horizontal) plane of the coil. This change occurs over a time interval of 0.1 s. a) (10 pts) Compute the change in the magnetic flux through the coil during this time interval. b) (10 pts) Determine the average induced potential in the coil during this time interval. c) (10 pts) How much current is induced in the coil?