Physics 9 Wednesday, April 2, 2014

Transcription

1 Physics 9 Wednesday, April 2, 2014 FYI: final exam is Friday, May 9th, at 9am, in DRL A2. HW10 due Friday. No quiz today. (HW8 too difficult for a quiz!) After this week: 2 weeks on circuits; then optics (light).

2 Changing the magnetic flux Φ B enclosed by a loop of wire induces an electric current to flow in the wire: I induced dφ B dt The minus sign means that the induced current flows in the direction that opposes the change in Φ B. Remember that the magnetic flux Φ B is proportional to the number of B field lines passing through a surface area A Φ B = B da = BA cos θ In this case A is the area enclosed by the loop of wire.

3 In the blue shaded region, B is uniform and points into the page. What is the direction of the induced current in loop (a) (the loop on the left) at the instant shown? (A) none (B) clockwise (C) counter-clockwise

4 In the blue shaded region, B is uniform and points into the page. What is the direction of the induced current in loop (b) (the middle loop) at the instant shown? (A) none (B) clockwise (C) counter-clockwise

5 In the blue shaded region, B is uniform and points into the page. What is the direction of the induced current in loop (c) (the loop on the right) at the instant shown? (A) none (B) clockwise (C) counter-clockwise

6 Here, the magnetic field B lies in the plane of this black loop, while the surface area vector A is, by definition, normal (i.e. perpendicular) to the plane of the loop. In this case, the magnetic flux Φ B through the loop area is (A) Zero (B) Not enough information (C) The magnetic field times the area of the loop

7 Suppose the magnetic field points upward and is perpendicular to the surface enclosed by the loop. In addition, the magnitude of the magnetic field increases with time. The induced current (as seen from overhead): (A) flows clockwise (B) flows counterclockwise (C) is zero (D) oscillates

8 Suppose the magnetic field points upward and is perpendicular to the surface enclosed by the loop. In addition, the magnitude of the magnetic field decreases with time. The induced current (as seen from overhead): (A) flows clockwise (B) flows counterclockwise (C) is zero (D) oscillates

9 I induced dφ B dt If we can mechanically cause Φ B to change with time, then we can use mechanical work to make electric current flow: generator, etc. This is the basis for how a power plant supplies electricity. There are several ways to do this. Let s first try shoving a bar magnet quickly into a loop (or coil) of wire.

10 I have a loop of wire, which is oriented so that its axis is in the left/right direction. (The dashed part of the loop is farther away from us than the dark part.) If initially there is no magnetic field nearby (and no current flowing in the wire), what is the magnetic flux Φ B through the coil?

11 Now suppose I start from far very far away, and I approach the loop from the right side, pointing the north end of a bar magnet at the loop. The magnetic flux ΦB through the loop (A) is increasing in magnitude, because the magnetic field near the loop grows stronger as the bar magnet moves closer. (B) is decreasing in magnitude. (C) is constant. (D) is zero.

12 Now suppose I start from far very far away, and I approach the loop from the right side, pointing the north end of a bar magnet at the loop. As I move the magnet closer to the loop, the current induced in the loop will flow (A) clockwise as seen from the magnet (my thumb points left). (B) counterclockwise as seen from magnet (thumb points right).

13 If instead I move the magnet farther away from the loop, the current induced in the loop will flow (A) clockwise as seen from the magnet (my thumb points left). (B) counterclockwise as seen from magnet (thumb points right).

14 If I approach the solenoid coil (which has its wire wound around N times) with the end of a bar magnet, it is analogous to the single loop of wire, but Φ B is multiplied times N. So moving the same magnet back and forth induces a larger current in the solenoid than in a single loop of wire, because we multiply by N 1200 for our 1200-turn solenoid. Induced current in one direction lights the green LED; induced current in the other direction lights the red LED.

15 A horizontal bar magnet spins around on a vertical axis through its center, at constant angular speed, so that first its north pole, then its south pole, then its north pole,... points toward the center of the green coil of wire. The induced current in the green coil of wire (A) flows clockwise (B) flows counterclockwise (C) is zero (D) oscillates sinusoidally

16 If the current in the big spool of wire flows counterclockwise (as seen from above), in which direction does the magnetic field point near the aluminum ring? (A) up (B) down

17 If the current in the big spool of wire starts from zero and rapidly increases in the counterclockwise (seen from above) direction, in which direction does induced current flow in the aluminum ring? (A) clockwise (as seen from above) (B) counterclockwise (as seen from above) (C) no current is induced

18 Current in big spool starts from zero and rapidly increases counterclockwise (seen from above). In which direction do the big spool s and the little ring s magnetic moments µ point? (A) Spool s µ points down; ring s µ points down. (B) Spool s µ points down; ring s µ points up. (C) Spool s µ points up; ring s µ points down. (D) Spool s µ points up; ring s µ points up.

19 The counterclockwise current in the spool makes an upward-pointing magnetic moment. The clockwise induced current in the ring makes a downward-pointing magnetic moment. That s like two north poles facing one another. Do two north poles attract or repel one another?

20 More quantitatively, changing the magnetic flux Φ B enclosed by a loop of wire induces a voltage ( emf ) E induced : E induced = dφ B dt The resulting current in the wire is proportional to the voltage E and inversely proportional to the wire s resistance R: I induced = E induced R = ( ) 1 dφb R dt We ll learn a lot more about resistance next week. By analogy with plumbing, a long, thin pipe offers a bigger resistance to water flow than a short, wide pipe. The voltage or emf E is like the height of the water tower, and the resistance R measures how long & skinny the pipe is.

21 I induced = E induced R ( ) 1 dφb = R dt The ring on the right has a gap, which stops the current from flowing. Its resistance is infinite! Will the ring still jump if there is no induced current? (And what if we instead try making the resistance smaller?)

22 One more thing from Chapter 29: inductance. We ll see it again in Chapter 33. Storing separated + and charge on a capacitor creates an electric field between the two plates. Energy is stored in this electric field. A capacitor s electrostatic potential energy is U E = 1 2 CV 2 Running an electric current through a coil of wire (e.g. a solenoid) creates a magnetic field. Energy is stored in this magnetic field. The inductance of a coil of wire relates the stored magnetic potential energy to the current: U B = 1 2 LI2

23 Physics 9 Wednesday, April 2, 2014 FYI: final exam is Friday, May 9th, at 9am, in DRL A2. HW10 due Friday. No quiz today. (HW8 too difficult for a quiz!) After this week: 2 weeks on circuits; then optics (light).