Potential Energy in Electric fields. AP Physics Monday 14.03.03 Standards: IIIaa4 Calculate the magnitude and direction of the force on a positive or negative charge placed in a specified field. Objective: SWBAT find the potential energy of a particle subject to a uniform electric field. Warm Up How strong is an electric field 200 m from a -1x10-3C charge? What is the Electric force if a -2x10-4C charge is placed at the above distance? Agenda Warm Up Check HW Review HW Potential Energy in Electric fields. Homework E#7

AP Physics Tuesday 14. 03. 04 Standards: IIIa AP Physics Tuesday 14.03.04 Standards: IIIa. Electric Potential Energy & Potential Objective: SWBAT find the electric potential due to an infinitely charged plate Warm Up Find the potential energy of a 5C charge that is 2m from a infinitely long positively charge plate? Agenda Warm Up Review HW Electric Potential Electrical Energy Inquiry` Homework E#8

AP Physics Wednesday 14.03.05 Standards: 2b electric potential of point charges Objective: SWBAT find the electric potential due to point charges. Warm Up Find the electric potential of an unknown electric charge in a uniform electric field of 0.25 N/c if you want to move it from a position of 5 meters away from the electric field source, to 2 meters away from the electric field source. b. Find the work done if the charge was -2C. Agenda Warm Up Review HW Electric Potential due to a charged particle. Electric Potential due to a charged particle inquiry Homework E#9

Equipotential Lines & Conductors Capacitors Warm Up Find the change in potential energy if a 30nC charge moves from 20m to 5m away from a -400nC charge. AP Physics Thursday 14.03.06 Standards: Students relate stored charge and voltage for a capacitor. Objective: SWBAT understand the charge distribution, electric field, and potential distribution & be able to solve problems involving capacitors. Agenda Warm Up Review HW Finish Inquiry Equipotential Lines & Conductors Capacitors Homework C#10

AP Physics Friday 14.03.07 Agenda Warm Up Review HW Capacitors Warm Up What is the electric potential difference between D and A? Standards: Students relate stored charge and voltage for a capacitor. Objective: SWBAT find the charge on a capacitor and describe the movements of charge through the parallel plates of a capacitor Is work done by the electric field or by you? Agenda Warm Up Review HW Capacitors Homework C#11

E#2 Coulomb’s Law Practice b. F=? q1=3.9x10-6C q2=2.2x10-7C r= 2.6x103m c. F=? q1=40μC q2=20μC r= 1x10-3 m d. F=200N q1=1x10-4C q2=2x10-4C r= ? b. F=? q1=8C q2=4C r= 2m 1.(4) In 1990, a French team flew a kite that was 1034 m long. Imagine two charges 2.0 nC and -2.8 nC, at opposite ends of the kite. Calculate the magnitude of the electric force between them. If the separation of charges is doubled, what absolute value of equal and opposite charges would exert the same electric force? 2. (2) Kalyan Ramji Sain, of India, had a mustache that measured 3.39 m from end to end in 1993. Suppose two charges, q and 3q, are placed 3.39 m apart. If the magnitude of the eletric force btween the charges is 2.4x10-6N, what is the value of q? 1μC=1x106C 1nC=1x109C

E#3 Force between multiple charges 200nC -30nC -20nC D 5 cm C 30cm A Find the net force on A Find the net force on C. 1. American athlete Jesse Castenada walked 228.930 km in 24 h in 1976, setting a new record. Consider an equilateral triangle with a perimeter equal to the distance Castenada walked. Suppose the charges are placed at the following vertices of the triangle: q1=-2.4 nC at the bottom right vertex, and q3=4.0 nC at the top vertex. Find the magnitude and direction of the resultant electric force acting on q1.

Practice: Charges in 2 Dimensions Find the Net Electric Force on the 1C Charge 1C -2C 4m 2m 3C

Electric Field Guided Practice Find the electric field at the red dot. 1μC 1μC 10m 5m

Electric Field Practice E#4 a. E=? q=1.6x10-6C r=20m b. Find the electric field at the red point. --->>> 2x103m 1μC 1μC c. Find the net electric field at the red point.--->>> 5m 1μC 10m 1. The world’s largest tires have a mass of almost 6000 kg and a diameter of 3.72 m each. Consider an equilateral triangle with sides that are 3.72 m long each. If equal positive charges are placed at the points on either end of the triangle’s base, what is the direction of the resultant electric field strength vector at the top vertez? If the magnitude of the electric field strength at the top vertex equals 0.145 N/C, what are the two quantities of charge at the base of the triangle?

Electric Field Lines Rules 1. Electric field lines always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object. 2. Electric field lines never cross each other. 3. Electric field lines are most dense around objects with the greatest amount of charge. 4. At locations where electric field lines meet the surface of an object, the lines are perpendicular to the surface.

Electric Field of an electron

Electric Field of a proton

Electric Field Lines Examples

Electric Field Lines Examples

Electric Field Lines Examples

Drawing & Understanding Electric Field Lines -- The idea behind drawing Electric field lines is easy. You calculate the electric field (like we did yesterday) at different points, with an emphasis on the direction of the electric field. If you find the direction of the Electric field at enough points, you will get something that looks very similar to the electric field diagrams from previous slides.

Guided Practice: Electric Field Diagrams Estimate the magnitude and direction of the electric field at each point shown. Use these vectors to draw an electric field diagram. + -

E#5 Electric Field Diagrams. Make an electric field diagram for the following configurations. Use the guided practice as your model. a. 1C 1C 2C -1C b. 36. The diagram above shows electric field lines in an isolated region of space containing two small charged spheres, Y and Z. Which of the following statements is true? (A) The charge on Y is negative and the charge on Z is positive. (B) The strength of the electric field is the same everywhere. (C) The electric field is strongest midway between Y and Z. (D) A small negatively charged object placed at point X would tend to move toward the right.(E) Both charged spheres Y and Z carry charge of the same sign.

E#7 Electrical Potential Energy a. F=? E= 40N/c q=-1.6x10-19C b. U=? q=2x10-6C E=0.5 N/c d=2.5 m c. We=? q=4x10-6C E=20 N/c d=1.2 m (2) The potential energy of an electron (q=-1.6x10-19C) increases by 3.3x10-15 J when it moves 3.5 cm parallel to a uniform electric field. What is the magnitude of the electric field through which the electron passes? (4) A charged particle moves through a distance of 9.35 m parallel to a uniform electric field. The electrical potential energy of the particle increases by 3.17x10-10 J as it moves. the electric field has a magnitude of 1.25x105N/C. a) What is the charge on the particle? (8) A negative ion (q=-4.8x10-19C) moves 0.63cm through a uniform electric field in a direction opposite to the direction of the field. The magnitude of the electric field is 279 volts per meter. What is the change in electrical potential energy of the ion?

E#8 Electrical Potential a. q1=20μC q2=40μC r=400 m U=? c. E=20 N/C d=5m V=? b. q=12nC r=3x10-2m V=? 1 (5) There is an electric field close to the surface of the earth. This field points towards the surface and has a magnitude of about 1.5x102 N/C. A charge moves perpendicularly toward the surface of Earth through a distance of 439 m, the height of the Sears Tower in Chicago, Ilinois. During this trip, the electric potential energy of the charge decreases by 3.7x10-8 J. What is the charge on the moving particle? What is the potential difference between the top of the Sears Tower and the ground? What is the electric potential of the charge at its final position? 2 (8) A negative ion (q=-4.8x10-19 C) moves 0.63 cm through a uniform electric field in a direction opposite to the direction of the field. The magnitude of the electric field is 279 volts per meter. What is the change in the electrical potential energy of the ion? What is the electric potential at the final position of the ion?

Electric Fields, Forces & Energy Inquiry Find the electric force between the charged balloon nearest to you and the infinitely long charged plate. ( You will need to take measurements.) Find the electrical potential energy between the infinitely charged plate and the nearest balloon. Find out how much work needs to be done to move your balloon to 1 meter away from the infinitely charged plate. Find the electrical potential at the point of the nearest golf ball. Find the electrical potential 1 m away from the infinitely charged plate.

Electric Fields, Forces & Energy Inquiry #2 Find the electric force between the two nearest charges. Find the magnitude of the electric field of the nearest charge to a point 2 meters away. Find the electrical potential energy between the nearest charge to you and the furthest charge from you. How much work would it take to move the furthest charge from #3 to a distance of 1 m from the closest charge How much potential is there between the nearest charge and the projector? How much will the potential change if some unknown charge is moved from the projector to 1 m away from your nearest charge?

E#9 Electrical Potential For Point Charges q1=2μC q2=6μC r=1x10-3m U=? b. q=6μC r=1x10-3m V=? c. q=6μC r2=1x10-3m r1=6x10-4 ΔV=? Find the electrical potential due to a 4nC charge at a point 25m away.? How much would the electrical potential change if wanted to move an unspecified charge to a distance of 2 m from the 4nC charge? Find the electric field 20 m away from a charge, if it has a voltage of 40 J/C. The electrical potential of an object 1Gm away from a 1x10-9 charge is approximately?

Eqipotential Diagrams The diagram above shows equipotential lines produced by an unknown charge distribution. A, B, C, D, and E are points in the plane. 88. Which vector below best describes the direction of the electric field at point A ? (A) (B) (C) (D) (E) None of these; the field is zero. 89. At which point does the electric field have the greatest magnitude? (A) A (B) B (C) C (D) D (E) E 90. How much net work must be done by an external force to move a –1 μC point charge from rest at point C to rest at point E ? (A) –20 μJ (B) –10 μJ (C) 10 μJ (D) 20 μJ (E) 30 μJ E points from high potential to low potential, perpendicular to equipotential lines A E is greatest in magnitude where V changes most rapidly with position (the largest gradient) which is where the lines are closest together. B W=qΔV =10μC Since the external force must push against the negative charge to keep it from accelerating and bring it to rest at point E, the work done by the external force must be negative.

E#10 – Conductors What is the electric potential inside of a conductor? What does an equipotential line tell us? How do the electric charges configure themselves in a conducting sphere? What is the magnitude of the electric field inside of a conductor?

Electrostatics Guided Practice 1974B5. The diagram above shows some of the equipotentials in a plane perpendicular to two parallel charged metal cylinders. The potential of each line is labeled. a. The left cylinder is charged positively. What is the sign of the charge on the other cylinder? b. On the diagram above, sketch lines to describe the electric field produced by the charged cylinders. c. Determine the potential difference, VA – VB , between points A and B. d. How much work is done by the field if a charge of 0.50 coulomb is moved along a path from point A to point E and then to point D?

Calculate the initial speed of the electron as it enters region I. 1985B3. An electron initially moves in a horizontal direction and has a kinetic energy of 2.0 x 103 electron–volts when it is in the position shown above. It passes through a uniform electric field between two oppositely charged horizontal plates (region I) and a field–free region (region II) before eventually striking a screen at a distance of 0.08 meter from the edge of the plates. The plates are 0.04 meter long and are separated from each other by a distance of 0.02 meter. The potential difference across the plates is 250 volts. Gravity is negligible. Calculate the initial speed of the electron as it enters region I. Calculate the magnitude of the electric field E between the plates, and indicate its direction on the diagram above. Calculate the magnitude of the electric force F acting on the electron while it is in region I. On the diagram below, sketch the path of the electron in regions I and II. For each region describe the shape of the path.