Monday, February 18, 2013 LESSON 7: ELECTRIC POTENTIAL

Monday, February 18, 2013 LESSON 7: ELECTRIC POTENTIAL Announcements HW #6 due today HW #7 due tomorrow Modern Phys #2 due tomorrow  Ignore th...
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Monday, February 18, 2013

LESSON 7:

ELECTRIC POTENTIAL

Announcements HW #6 due today HW #7 due tomorrow Modern Phys #2 due tomorrow  Ignore the lab simulation info on HW sheet

HW Quiz TUESDAY!!! Lunch Bunch this week:  Photoelectric Lab simulation (Details to come Tuesday)

AP Physics B Course Objectives III.A.2. Electric Field & Electric Potential b) Students should understand the concept of electric potential, so they can: (1) Determine the electric potential in the vicinity of one or more point charges.  (2) Calculate the electrical work done on a charge or use conservation of energy to determine the speed of a charge that moves through a specified potential difference.  (4) Calculate the potential difference between two points in a uniform electric field, and state which point is at the higher potential.  (5) Calculate how much work is required to move a test charge from one location to another in the field of fixed point charges.

Student Objectives Students will be able to: 1) 2)

read and interpret equipotential maps. apply energy conservation to electrostatic situations

Review: Electric Potential Energy Potential energy configuration of two charges For spherically symmetric charges

Electrostatic forces spontaneously do positive work to decrease EPE. External forces are necessary to increase EPE.

EPE and Work For ANY force: W = F ∆r cos θ For electrostatic forces: WE = FE ∆r cos θ For conservative forces: Wc = - ∆U

Electrical Potential and Potential Energy Electric Potential is Electric Potential Energy per unit charge.

UE V q

Electric Potential Difference is the change in electric potential energy per unit charge.

U E V  q

Unit: Volts

Common term: voltage

Electric Potential Difference r = 1.0 m q1 = 1.0 C



1.0 1.0 1.0

ΔU = UB – UA ΔU = (1/2 k – 1 k) ΔU = –1/2 k

r = 1.0 m q2 = 1.0 C

B

A





1.0 1.0 2.0

1⁄2

ΔVAB = ΔU / q2 ΔVAB = (-1/2k) / (1.0 C) ΔV = –(1/2 k) V

The positive charge naturally moves in the direction of DECREASING U. Positive charges move to DECREASE their electric potential (V).

Electric Potential Difference rA = 1.0 m

q1 = 1.0 C

rB = 0.5 m

B

q2 = -1.0 C



1.0 1.0 1.0

ΔU = UB – UA ΔU = (– 2 k – (– 1 k)) ΔU = – k

A





1.0 1.0 0.5

2

ΔVAB = ΔU / q2 ΔVAB = (- k) / (-1.0 C) ΔV = +(k) V

The negative charge naturally moves in the direction of DECREASING U. Negative charges move to INCREASE their electric potential (V).

Electrical Potential and Potential Energy Spontaneous movement will decrease UE.

∆V = ∆U / q Positive charges like to DECREASE their potential (V < 0) Negative charges like to INCREASE their potential. (V > 0)

Sample problem 7.1: A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?

Electric Potential due to multiple charges  The electric potential at any point in space is the scalar sum of the potentials due to each charge

V = V1+ V2 +V3

Electric Potential of Spherically Symmetric Charges

Characteristics of Equi-potential Surfaces

Characteristics of Equipotential Surfaces

About Equipotential Maps… 1. The potential difference between any two points along the same equipotential line is zero. 2. Electric field lines always point in the direction of decreasing electric potential. 3. Electric field lines are always perpendicular to the equipotential lines. 4. The closer the equipotential lines are to one another, the steeper the gradient of the potential.

Sample problem 7.2: Suppose a 2mC charge is moved from point b to point c. a) What is its potential energy change? b) What about if a -3mC charge does the same thing?

Conservation of Energy Review In a conservative system, energy changes from one form of mechanical energy to another.

U1  K1 U2  K2

Sample problem 7.3: If a proton is accelerated through a potential difference of -2,000 V, what is its change in potential energy?

How fast will this proton be moving if it started at rest?

Sample Problem 7.4: A proton at rest is released in a uniform electric field. How fast is it moving after it travels through a potential difference of -1200 V? How far has it moved?

Sample Problem 7.5: Suppose an electron is moving at 200,000 m/s when it enters a region where its electric potential begins changing. Through what potential difference must it travel before it comes to rest (assuming its motion is aligned with the field).