Exam1_Review

PHYS:1512 9/18/2023

Announcements • HW 4 due on Sunday – I recommend trying it out before the test. Most problems won’t take a long time to do, and are a good source of practice for the exam • Reminder: no labs or discussion this week • Discussion questions (with answers) for chapter 21 on ICON

• Random assigned seating (3 versions of the exam) • Do not open or begin exam until 9:30 when you are signaled to begin. • Answer form will be inside, and last page is a tear-off equation sheet (double-sided). • Bring a pencil, eraser, calculator, ID , but no other assistance – backpacks closed while you are in the room. • If your cell phone is out = fail exam. Turn them off! • No hats • No talking with neighboring students – ask a TA for clarification if needed • Return answer sheet and the exam itself with your name on it • Show ID

Format of the Exam • 16 multiple choice questions on material covered from Chapter 18-21 • Types of questions: • Conceptual • Scaling • Plug-and-chug: (which you have to recognize and understand the inputs) and straightforward evaluation • A few short work-out questions • Your homework problems, the lecture slides, and the discussion problems are a good guide to the material covered • Practice assignments are good exercise

Example of Scaling Problem • HW #2, Problem 3 • An empty parallel plate capacitor is connected between the terminals of a 19.0-V battery and charges up. The capacitor is then disconnected from the battery, and the spacing between the capacitor plates is doubled. As a result of this change, what is the new voltage between the plates of the capacitor? • 38.0-V

Example of Plug and Chug • HW 2, Problem 7 • An electric blanket is connected to a 120-V outlet and consumes 190 W of power. What is the resistance of the heater wire in the blanket? • 75.8 Ω

Equation Sheet PHYS:1512 Possibly Useful Equations Exam 1 F = k | q 1 || q 2 | r 2 ~ E = ~ F q 0 Φ E = ⌃ ( E cos φ ) Δ A = Q enc ✏ 0 W AB = EPE A - EPE B V = EPE q 0 Δ V = Δ (EPE) q 0 = - W AB q 0 E = - Δ V Δ s E = k | q | r 2 V = kq r q = CV  = E 0 E Energy = 1 2 qV = 1 2 CV 2 E = q ✏ 0 A = σ ✏ 0 E = V d C = ✏ 0 A d ⌧ = RC q = q 0 h 1 - e - t/ ( RC ) i q = q 0 e - t/ ( RC ) I = Δ q Δ t V = IR P = IV R = ⇢ L A R eq = R 1 + R 2 + . . . 1 R eq = 1 R 1 + 1 R 2 + . . . B = F | q 0 | ( v sin ✓ ) r = mv | q | B F = ILB sin ✓ ⌧ = NIA ( B sin φ ) B = μ 0 I 2 ⇡ r B = N μ 0 I 2 R B = μ 0 nI e = 1 . 60 ⇥ 10 - 19 C m e = 9 . 11 ⇥ 10 - 31 kg m p = 1 . 675 ⇥ 10 - 27 kg k = 1 4 ⇡✏ 0 = 8 . 99 ⇥ 10 9 N · m 2 / C 2 ✏ 0 = 8 . 85 ⇥ 10 - 12 C 2 / ( N · m 2 ) μ 0 = 4 ⇡ ⇥ 10 - 7 T · m / A 1 eV = 1 . 60 ⇥ 10 - 19 J In what situations do these equations apply? What do the variables mean? What equations are missing? What conceptual information do you need in addition to this?

Electrostatic Force and Electric Field Coulomb’s Law: force between charges • Use absolute magnitude then decide direction Electric Field: exists in space, even in charge not there to feel a force • What direction would a positive charge feel a force in, if it were placed there? Gauss’ Law: General way to find electric field from charges • Always applicable, useful only when symmetry exists Not given: For a sphere, Φ ! = ࠵?࠵? = ࠵? "#$ ࠵? %

• Exam 1 Practice – Chapter 18, Problem 14 • A solid, conducting sphere of radius a carries an excess charge of +6 µC. This sphere is located at the center of a hollow, conducting sphere with an inner radius of b and an outer radius of c as shown. The hollow sphere also carries a total excess charge of +6 µC. • Determine the excess charge on the inner surface of the outer sphere (a distance b from the center of the system). • -6 µC Outer surface? +12 µC

Charged Conductor At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor. At equilibrium under electrostatic conditions, the electric field is zero at any point within a conducting material. The conductor shields any charge within it from electric fields created outside the conductor. Not shown on equation sheet:

• What is the direction of the electric field at B? • At which of the labeled points will the electric field have the greatest magnitude? • What is the magnitude of the electric field at point A? • How much work needed to move a +4 µC charge from G to F to A? The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A , B , C , ..., I .

Special Cases Parallel Plate Capacitor Point Charge Φ ! = ࠵?࠵? = ࠵? "#$ ࠵? %

Example of Work-Out • Exam 1 Practice – Chapter 19, Question 8 • Three point charges – Q , – Q , and +3 Q are arranged along a line as shown in the sketch. • !" # Not given on equation sheet: potentials add ࠵? = ࠵? ! + ࠵? " + ࠵? # + ⋯

Capacitors Capacitors in General Capacitance is a geometric and materials property: doesn’t depend on q, V – it sets them Time constant A dielectric material decreases E field, increases capacitance Amount of energy stored in a capacitor Capacitors in RC Circuits Charge on plate: charging Charge on plate: discharging