Danger High Voltage! Your friend starts to climb on this... You shout Get away! That s High Voltage!!! After you save his life, your friend asks:

Transcription

1 Danger High Voltage! Your friend starts to climb on this... You shout Get away! That s High Voltage!!! After you save his life, your friend asks: What is Voltage anyway?

2 Voltage... Is the energy (in Joules) that a unit of (+) charge (1 Coulomb) would have at a given location. The formal term for it is: The Electric Potential (...or sometimes just the Potential ) Voltage is measured in Volts (V) = Joules/Coulomb (J/C) ΔU = q ΔV

3 Example 20-1 (p.694) YOUR TURN: A and B are two locations within a capacitor (not charged particles) 1. ) Is the Voltage higher at point A or B? 2.) Where does an electron have higher potential energy, A or B?

4 Free Floating Charges: Positive vs. Negative Electric Field: Positive charges move (ie accelerate) in the direction of the E field. Negative charges move in the opposite direction of the E field. Electric Potential: Positive charges accelerate in the direction of decreasing electric potential (V) Negative charges accelerate in the direction of increasing electric potential (V). But, in both cases, the freely-moving charge loses potential energy (U), and gains kinetic energy.

5 Conservation of Energy The total energy of a system never changes. (Initial Total Energy = Final Total Energy) Total Energy = Kinetic (1/2 mv 2 ) + Potential (U) +... Ugravity = m g h Uspring = 1/2 k x 2 Uelectric = q V = q E d v = velocity V = Voltage If there s before and an after, then total energy (ET) doesn t change: ETA = ETB

6 ETA = ETB We can use this to determine the velocity of a particle released in an electric field. Example: What would be the speed of a proton released from rest, at the positive terminal of a 9V battery when it reached the negative terminal? How much kinetic energy would this proton have as it hit.

7 New Unit of Energy: electron Volts (ev) A free electron in an electric field will pick up kinetic energy. This allows us to define a new unit of energy. Suppose two places have a voltage difference of 1 Volt. (ΔV = 1 V). If we allow one electron to accelerate through this voltage difference, it will gain kinetic energy (KE). How much? It gains as much KE as the PE it lost: PE = U = q * ΔV = (1 e)*(1v) This amount of energy is called one electronvolt (symbol: ev). The electron-volt is a unit of energy: Chemical Bonds have energy ~ 1 ev X-rays have energy : ~10,000 ev (10 KeV) Nuclear reactions energy: ~1,000,000 ev (MeV)

8 Potential Energy of Charges You must expend energy to push a test charge (+q0) close to a charge (+q) at the origin. So, q0 s potential energy depends on distance (r) inversely. If its distance increases... r A Then its potential energy will decrease by: (fixed) Chemical Energy is just the re-arrangement of charged particles.

9 Voltage around a Charge Now, using our definition: ΔV = ΔU/ q 0 We can compute the Voltage at any location, a distance r from a a point charge (+q) : VA-VB = kq/ra - kq/rb Figure 20-4 Only Changes in V matter. We can define V=0 wherever we want.

10 Important Convention: We define V=0 at r=infinity r B =infinity; V B = 0 V A - 0 = kq/r A - 0 The Voltage produced by at charge q, a distance r away is: V = k q/r Figure 20-4 (Note: q can be + or - ; r is always +)

11 Superposition Principle E and V 1. The Electric Field Vector (E) at a given location is the vector sum of all electric fields at that point. 2. The Voltage (V) at a given location is the scalar sum of the Voltages at that point due to all nearby charges. We can use diagrams to show either the E field or V at all points.

12 Consider 2 positive charges on the x-axis: What is the Voltage as a function of x, V(x)?

13 Positive everywhere. (and sometimes infinite!)

14 Electric potential of two point charges of opposite sign.

15 Equipotential Surfaces & Electric Field On a map, contours mark constant elevation; a ball will roll downhill: perpendicular to the curves. The closer together the curves, the steeper the slope.

16 Heat maps are another form of contour maps

17

18 Electric Field due to a point charge. 2-D Suppose the Voltage at Point X is: V = 2 Volts. X Where else would the electric potential be the same? draw

19 Lines that connect points of equal Voltage (V) are called: Equipotential lines They are like contours of elevation on a topographic map.

20 Figure 20-7 Equipotential lines on a capacitor. Where are they the highest?

21

22 Figure 20-5A Surface Plot

23 Figure 20-5B