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Midterm

# 198 Midterm: Exam 1 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 I: E1-E10 I. E1- Electric Fields βββ 1 π1 2 1 9 2 2 A. |πΉ π = 4ππ0 π2 , where π = 4ππ0 = 8.99 x 10 Nm /C 1. Opposite signs Β» attractive 2. Same signs Β» repulsive βββ β B. |πΉ π = ππΈ 1. Generally electric field lines point away from + charges, towards negative charges 1 π 2. πΈ = 4ππ π2 πΜ 0 3. Superposition principle: total electric field is the vector sum of each individual field, unaffected by presence of other charges II. E2- Charge Distributions A. Dipoles 1. πΈ = 1 π π = 1 πβπβ 2ππ0π3 2ππ0π3 a. Where s is the separation between charges, r = distance from center of dipole b. Where p ie the dipole moment vector, direction of positive particle with respect to negative particle βπββ = ππ  + Μπ B. Electric Polarization β β 2πΌ|πΈ| π 2 1. πβπββ = πΌπΈ, πΈ = (4ππ0) π 5(higher ο‘ is higher polarizability) C. Calculating Electric Fields 1. Divide distribution into small bits to model as particles 2. Determine each bitβs charge 3. Calculate the field vector that each point contributes at P 4. Sum the field vectors over all bits D. Other Charge Distributions 1. Charge of an Infinite Plane β π a. πΈ = 2π0πΜ (perpendicular to source plane at P, w/ constant charge per unit area ο³) 2. Spherical Shell a. Inside the shell, πΈ = 0 1 π b. Outside the shell: πΈ = 2πΜ 4ππ 0 3. Infinite Line β 1 π a. πΈ = 2ππ0π πΜ 4. Along the axis of a ring with uniform charge Q a. πΈ = ππ§π (fields cancel in x and y directions b/c of circle symmetry) π (π§ +π )3/2 III. E3- Electric Potential A. Electric Potential Energy π π π π = ( 1 + 2 + β―) π 4ππ 0 |π1 π2| B. Electric Potential ππ(π₯,π¦,π§) 1 π 1. π π₯,π¦,π§ =) π = 4ππ |π| βππ 2. In a uniform field: βπ = = βπΈβπ, π a. For any field: βπ = β πΈ β«πβ b. πΈ π₯,π¦,π§ = ββ π 3. Shell Theorem 1 π a. Inside a shell, potential is constant: π = 1 π 4ππ0π b. Outside a shell: π = 4ππ0|π| IV. E4- Static Equilibrium A. Static Equilibrium 1. Charge is at rest within conductorβs boundaries, πΈ = 0 inside of surface a. Potential is the same at all points inside an isolated conducting region (βο¦ =0) b. πΈ at all points on conductorβs surface must point perpendicular to that surface c. Conducting interior of a conducting object must be electrically neutral in static eqβb 2. Can isolate an object form an external field using a conducting container (Farraday cage), protrusions on a surface have a higher charge density B. Parallel Capacitor π π΄ 1. Capacitance, πΆ = βπ = π 0π  a. Large C holds more charge b. C depends only on size, shape, arrangement of plates c. A is the area of plates, s is the distance between the plates π 2. Between 2 plates, πΈ = (where ο³ = Q/A) and βπ = β|πΈ|π  β 2 π0 a. |πΉ| = π 20 π΄ 1 β 2 b. Electric field density Β΅π= π2|πΈ0 1 2 c. Energy stored in capacitor = U = πΆ|2π| V. E5- Current A. Current Density (π½) 1. π½ = ππ£ = πππ = ππ( )π = ππ ( )π = ο³ πΈ2 πΈ β π π π π πΆ ππΈβ a. Drift velocity π£ π π π, Drude theory uses π estimation b. n is the number density of carriers, π =-1ime between collisions c. ο³ iπΆ the conductivity in units of (Ξ©π) B. Flux βπ 1. πΉππ’π₯ = = π π£ |π΄| = π π£ |π΄|πππ ο± = π½ β’ π΄ βπ a. Total flux through a surface, π = β« π½ β’ ππ΄ π π 2. Current (I) a. πΌ = β«π π½ β’ ππ΄, expresses the rate at which charge flows through a given surface b. For a uniform wire, I = JA (A = cross sectional wire area) c. Flux is positive if charges move forward, negative if backwards through a surface
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