Physics II: Electricity & Magnetism Sections 23.4, 23.7, & 23.8

Tuesday (Day 8)

Warm-Up Tues, Mar 10 Complete the following Graphic Organizers: HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Warm-Up Tues, Mar 10 Complete the following Graphic Organizers: Electric Field Lines and Equipotential Lines (Section 23-5) Methods for Determining E and V (23-2, 23-3, 23-4, & 23-7) Place your homework on my desk: Equation for rm for concentric cylinders For future assignments - check online at www.plutonium-239.com

Essential Question(s) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? How do we use integration and the principle of superposition to calculate the electric potential of a thin ring of charge on the axis of the ring? How do we use integration and the principle of superposition to calculate the electric potential of a semicircle of charge at its center? How do we use integration and the principle of superposition to calculate the electric potential of a uniformly charged disk on the axis of the disk?

Vocabulary Electric Potential Potential Difference in Potential HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Vocabulary Electric Potential Potential Difference in Potential Potential Difference Volt Voltage Equipotential Lines Equipotential Surfaces Electric Dipole Dipole Moment Electron Volt Cathode Ray Tube Thermionic Emission Cathode Anode Cathode Rays Oscilloscope

Agenda The Potential Due to Any Charge Distribution HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Agenda The Potential Due to Any Charge Distribution Steps to Determine the Potential Determine V from point charges A Ring of Charge A Disk of Charge A Horizontal Line of Charge Complete the following: Web Assign Problem 23.7 Electrostatics Lab #5: Potential If time permits, discuss E Determined by V

Potential Due to Any Point Charge HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Potential Due to Any Point Charge Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector.

Potential Due to Any Point Charge HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Potential Due to Any Point Charge We will now have the ability to sum up all of the point charges to determine the total potential for any charge distribution.

HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Steps to Determine the Potential Created by a Uniform Charge Distributions Graphical: Draw a picture of the object and 3-D plane. Label the partial length, area, or volume that is creating the partial potential. Determine the distance from the charged object to the location of the desired potential and label all components and lengths. Mathematical: Write the formula for V(dq). Note: Because potential is scalar, there is no need to resolve any components. Write the total charge density and solve it for Q. Write the charge density in relation to the partial charge and solve it for the partial charge (dq). Set up the integral by determining what key component(s) change. †Solve the integral and write the answer in a concise manner. †See the instructor, AP Calculus BC students, or Schaum’s Mathematical Handbook.

V: Uniformly Charged Ring ( 0  2) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Ring ( 0  2)

V: Uniformly Charged Disk (0R) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Disk (0R)

V: †Uniformly Charged Horizontal Wire (dd+l) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: †Uniformly Charged Horizontal Wire (dd+l)

HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Special Potentials

V at center of a Uniformly Charged Semicircle ( 0  ) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V at center of a Uniformly Charged Semicircle ( 0  )

HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Summary Potential at the center of a uniformly charged semicircle () HW (Place in your agenda): Web Assign Problems 23.7 Future assignments: Lab #5: Potential Lab Report (Due in 5 classes)

Wednesday (Day 9)

HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Warm-Up Wed, Mar 11 Write down how you would explain to a blind man how to draw the integral sign. Place your homework on my desk: Equation for the Potential at the center of a uniformly charged semicircle () For future assignments - check online at www.plutonium-239.com

Essential Question(s) HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? How do we differentiate the electric potential to calculate the electric field of a thin ring of charge on the axis of the ring? How do we use differentiate the electric potential to calculate the electric field of a semicircle of charge at its center? How do we differentiate the electric potential to calculate the electric field of a uniformly charged disk on the axis of the disk?

Vocabulary Electric Potential Potential Difference in Potential HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? Vocabulary Electric Potential Potential Difference in Potential Potential Difference Volt Voltage Equipotential Lines Equipotential Surfaces Electric Dipole Dipole Moment Electron Volt Cathode Ray Tube Thermionic Emission Cathode Anode Cathode Rays Oscilloscope

HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? Agenda Determine E from V for the following A Ring of Charge A Disk of Charge A Horizontal Line of Charge Potential Determinations for Electric Dipoles Complete the following: Web Assign Problem 23.8 - 23.12 Electrostatics Lab #5: Potential

Determine E from V Recall that V is the area under the E(r) graph, HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? Determine E from V Recall that V is the area under the E(r) graph, Therefore, E is the slope of the V(r) or V(x,y,z) graph Therefore dV is the infinitesimal difference in potential between two points a distance dl apart, and El is the component of the electric field in the direction of the infinitesimal displacement dl. The component of the electric field in any direction is equal to the negative of the rate of change of the electric potential with distance in that direction. The quantity dV/dl is called the gradient of V in a particular direction. If the direction is not specified, the term gradient refers to that direction in which V changes the most rapidly; This would be the direction of E at that point

HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? Determine E from V We use the gradient to solve for E from V Where the V is the area under the E(r) curve, E is the slope of the V(r) or V(x,y,z) curve Therefore dV is the infinitesimal difference in potential between two points a distance dl apart, and El is the component of the electric field in the direction of the infinitesimal displacement dl. The component of the electric field in any direction is equal to the negative of the rate of change of the electric potential with distance in that direction. The quantity dV/dl is called the gradient of V in a particular direction. If the direction is not specified, the term gradient refers to that direction in which V changes the most rapidly; This would be the direction of E at that point

E Determined by V: Uniformly Charged Ring ( 0  2) HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? E Determined by V: Uniformly Charged Ring ( 0  2)

E Determined by V: Uniformly Charged Disk (0R) HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? E Determined by V: Uniformly Charged Disk (0R)

E Determined by V: †Uniformly Charged Horizontal Wire (dd+l) HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? E Determined by V: †Uniformly Charged Horizontal Wire (dd+l)

HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? Determination of V from E: Spherical Insulator of Uniform  (r < r0) E + + + + + + + r0 + + + + + + + + dr + +

HOW DO WE APPLY DIFFERENTIATION TO ELECTRIC POTENTIALS TO DETERMINE THE ELECTRIC FIELD? Special E-Fields

Essential Question(s) HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? How do we use the potential function for a point charge to calculate how much work is required to move a test charge from one location to another in the field of fixed point charges? How do we use the potential function for a point charge to calculate how much work is required to move a set of charges into a new configuration?

Work Required to Move Charges HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Work Required to Move Charges So far, we have discussed the work done by the electric field to move a positive test charge in the direction of the electric field (possibly to infinity and beyond) Examples: Dropping a ball A rollercoaster going down a hill Now we will look at the external work required to move a positive test charge in the opposite direction of the electric field and therefore storing electrical potential energy. Lifting a ball in the air. A roller coaster ascending the initial hill.

The Electron Volt, a Unit of Energy HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS? The Electron Volt, a Unit of Energy One electron volt (eV) is the energy an electron gains when it is accelerated though a potential difference of one volt. Electron volts are useful in atomic, nuclear, and particle physics.

Electric Potential Energy HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Electric Potential Energy We will also have the ability to sum up all of the point charges to determine the total potential energy for any charge distribution. Today is that day . . .

Electric Potential Energy HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Electric Potential Energy

Electric Potential Energy HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Electric Potential Energy L L

Electric Potential Energy HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Electric Potential Energy How much energy is required to bring 4 +5 C charges into a square of sides of length = 2.0x10-9 m? Will it have a positive or negative value? Why?

Electric Potential Energy HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Electric Potential Energy How much energy is required to bring 4 charges (q1=q4=+5 C; q2=q3=-5 C) into a square of sides of length = 2.0x10-9 m? How do you think it will compare to the previous example? Will it have the same value, less, or more? Why?

Electric Potential Energy HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Electric Potential Energy What is the mathematical relationship between the number of charges and the size of the equation? n=1; 0 terms n=2; 1 term n=3; 3 terms n=4; 6 terms How many terms will n = 5 have? n =10?

HOW DO WE DESCRIBE AND APPLY THE POTENTIAL FUNCTION FOR A POINT CHARGE? Summary How many terms will n = 42 have? HW (Place in your agenda): Web Assign Problems (except for 23.10, 23.14, 23.15) Future assignments: Lab #5: Potential Lab Report

Supplemental Derivations HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? Supplemental Derivations Ring (Additional Approaches) Vertical Lines Disk (Additional Approaches)

V: Uniformly Charged Ring ( 0  2) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Ring ( 0  2)

V: Uniformly Charged Ring ( 0  2) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Ring ( 0  2)

V: Uniformly Charged Disk (0R) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Disk (0R)

V: Uniformly Charged Disk (0R) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Disk (0R)

V: Uniformly Charged Disk (0R) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Disk (0R)

V: Uniformly Charged Vertical Wire (–L/2+L/2) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Vertical Wire (–L/2+L/2)

V: Uniformly Charged Vertical Wire (0  L) HOW DO WE APPLY INTEGRATION AND THE PRINCIPLE OF SUPERPOSITION TO UNIFORMLY CHARGED OBJECTS? V: Uniformly Charged Vertical Wire (0  L)