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Midterm

# 198 Midterm: Exam 2 Study Guide Premium

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School
Washington University in St. Louis
Department
Physics
Course
Physics 198
Professor
Seidel
Semester
Spring

Description
Physics 198 Exam II: E16-E18 and Q1-Q5 I. E15 โ Maxwellโs Equations A. Ampere-Maxwell Law ๐๐ธ 1. โรB โ ยต ๐ 0 = ยต 0 (๐ฝ = ๐๐ฃ, density of charge * velocity) ๐๐ก ๐๐ต ๐๐ต ๐๐ต 2. Consistent with Gaussโs Law: โรE = 0 = ๐ฅ + ๐ฆ + ๐ง ๐๐ฅ ๐๐ฆ ๐๐ง a. Magnetic monopoles canโt exist B. Faradayโs Law for a static field ๐ ๐ ๐ธ๐งโ ๐ธ ๐ฆ ๐๐ฆ ๐๐ง โโ โโ ๐ ๐ 1. โรE = ๐๐ง ๐ธ๐ฅโ ๐๐ฅ ๐ธ๐ง = 0 ๐ ๐ [ ๐ธ ๐ฆ ๐ธ๐ฅ] ๐๐ฅ ๐๐ฆ C. Maxwellโs Equations 1. โ โข E = ๐ ๐0 ๐๐ธ 2. โรB โ ยต ๐ 0 ๐๐ก = ยต 0 3. โ โข B = 0 ๐๐ต 4. โรE +โ ๐๐ก = 0 II. E16 โ Faraday Law ๐๐ต A. โรE = โ ๐๐ก B. For a solenoid 1. Electric Field 1 ๐๐ง a. 2 ๐๐ก ๐ข (for u < R, R = radius of coil) 1 ๐๐ต ๐ง ๐ 2 b. โ (2 ๐๐ก ) ๐ข (for u > R) 2. EMF of a conducting loop a. ๐ = ๐ค = โฎ E๐r = โ( ๐๐ต๐ง)๐๐ 2 ๐ ๐๐ก C. Flux Through a Closed Loop 2 1. Flux, ฮฆ =B โฎ B๐A = ๐ต ๐๐๐ง(for a circular loop) ๐ โโ 2. ๐ = โ ๐๐ก(ฮฆ B for constant B a. Determines the direction of induced EMF 3. Lenzโs Law a. An induced current seeks to oppose the charge that create it b. Creates force opposing the motion D. Current and Materials 1. Superconductor can occur at very low temperatures, has effectively zero resistance 2. Maintains zero E and B (flux through disc remains zero) internally, but current can flow through a. Requires no energy to maintains current inside, flowing current doesnโt dissipate energy when R = 0 III. E17 โ Induction A. Induction and Current ๐2 1. Inductance (L) = ยต ๐0 ( ) ๐ a. Note, length of wire (2nrN = d) is fixed ๐ฝ b. Inductance in units of โHenryโ (H) = [Vโขs/A] = ฮฉ๐  = ๐ด2 2. Self-induced EMF is related to the rate of change in current by inductance a. ๐ = ๐ฟ| ๐๐ผ|, | | = โ ๐ผ ๐๐ก ๐๐ก ๐ฟ b. Inductance (L) is a fixed characteristic based on shape, size, # of turns in coil loop 3. Energy ๐๐ 2 2 โ2 ๐ก a. ๐๐ก = ๐ = ๐ผ ๐ = ๐ผ ๐๐0 ๐ฟ ๐โ 1 2 b. ๐ = 2๐ผ 0 1 2 1 2 c. Remember energy densities: ยต = ยต๐ต|B | an0 ยต0= ๐ |E| ๐ 0 โโ 2 2 2 ๐ต ๐๐ ๐ 2 |B0| d. ๐ = 2๏ญ |B0| , and thus energy per unit volume, ๏ญ =๐ต 2๏ญ 0 2 0 1 2 |B| e. ยต ๐ธ๐ = (๐ |0| + ) 2 ยต0 B. Applications of Induction 1. LC Circuit a. Capacitor connected to a inductor with low resistance b. All energy oscillates from E of capacitor to B of coil 2 c. ๐ |= โ๏ฆ = ๐ | | = ๐ฟ| ๐๐ผ| ๏  |๐|= ๐๐ผ = ๐ ๐ ๐ถ ๐ฟ ๐๐ก ๐ฟ๐ถ ๐๐ก ๐๐ก 2 ๐ ๐๐ผ d. By the loop rule, โ๏ฆ ( )๐ถโ ๐ผ๐ โ ๐ฟ ๐๐ก= 0 1 e. ๐ ๐ก = ๐ cos0๐๐ก), where ๐ = โ๐ฟ๐ถ 2. Transformers a. Setup: 2 independent coils, wrapped around each other, one attached to an A/C source where ๐ ๐ก = ๐ si0(๐๐ก) b. ๐ = ๐ ๐ผ, the smaller the EMF, the greater the current must flow through to supply power 2 ๐0 c. Average power: ๐ ๐ก = โ 2๐๐ sin 2๐๐ก ) 0 1 d. ๐ผ ๐ก = ๐ฟ๐ sin(๐๐ก โ ๐)2 IV. E18 โ Electromagnetic Waves A. Properties 1. Any disturbance in the EM field travels away from source at the speed of light 2. A disturbance in B is always accompanied by a disturbance in E: ๐ธ = โ๐๐ต ๐ง ๐ฆ a. E and B are perpendicular at every point b. E = pointer finger, B = middle finger, thumb = velocity of propagation c. EM waves are transverse, have no field components in the direction of motion d. EM waves have 2 independent polarizations B. Calculations โโ2 1. Energy density: ยต ๐ธ๐ = ๐ |0| โโ2 1 2. Average EM wave intensity = ๐๐ [|E0 ] (๐๐ = 377 ฮฉ) ๐๐ฃ๐ 0 โ 1 โโ โโ โ 1 โโ โโ ๐ถ โโ2 3. Poynting Vector (intensity), S = ยต0EรB, |S| = ยต0|E||B| = ๏ญ B | = ๐๐ 0E| 0 4. Accelerated Charges Produce EM Waves ๐ aโ|2sin ๏ฑ] ๐ a. ๐ = ๐๐ฃ๐ ( sin ๏ฑ ] = for a sphere) ๐ธ๐ 4๐๐0๐3 ๐๐ฃ๐ 3 2 ๐ a | ๐ a | b. Rate of energy radiation by the Larmor Formula:
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