Physics 51 Final Exam Study Guide(6)

Physics 51 Final Exam Study Guide(6) - Physics 51 Concept...

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Physics 51 "Study Guide" for Final ("Laundry List" of important concepts) Todd Sauke Concept (important concepts in bold; vectors also shown in bold ) Symbol or Equation Prerequisites: Physics quantities are typ. either scalars or vectors (magnitude & direction) components of vectors add From mechanics , total external force on a body = mass x acceleration Σ F ext = m a (SI newton, "N") Mass (SI kilogram, "kg") resists change in motion (via " momentum" , p ) p = m v , F ext = d p /dt A mass moving in a circle undergoes centripetal acceleration a centr = v 2 / r Conservation of linear momentum : Isolated system ( Σ F ext = 0) Æ Δ p =0 ; p f = p i m 1 v f1 + m 2 v f2 = m 1 v i1 + m 2 v i2 A moving mass has energy of motion, " Kinetic Energy " (SI joule, "J") KE = ½ m v 2 (a scalar) A spring being compressed pushes back proportional to compression F = - k x A compressed spring has energy of compression, elastic " Potential Energy " U = ½ k x 2 For conservative forces, mechanical energy is conserved E = KE+PE = constant (W nc =0) Electromagnetics: Electric Charge is the fundamental quantity in Electrostatics Q (SI coulomb, "C") Charge is conserved, quantized, and comes in "positive" and "negative" e = 1.602 x 10 -19 C Like charges repel ( radially ); opposite charges attract; Coulomb's Law F = (1/4 π ε 0 ) q 1 q 2 / r 2 The constant ε 0 is numerically related (by definition) to the speed of light, c ε 0 = 10 7 / (4 π c 2 ) = 8.854 x 10 -12 All "normal" matter is made up of protons, neutrons and electrons m p = 1.67 x 10 -27 kg Protons have +e charge; electrons have –e. Their mutual attraction holds m e = 9.11 x 10 -31 kg everything together. In a conductor, electrons are free to move around. Total force ( vector ) is the vector sum of individual forces ( superposition ) F = Σ F i The Electric field vector is the force per unit charge on a "test charge", q 0 E = F 0 / q 0 F = q E For distributions of charge (eg. λ , σ ), vector integrate over the distribution E = d E = dq / (4 π ε 0 r 2 ) ř Field lines provide a graphical representation of E (and B ) fields E strong where lines are dense An Electric Dipole is a separation of equal magnitude, opposite charges p = q d ( d =separation - Æ +) An Electric Dipole, p , in an Electric field, E , experiences a torque τ = p x E τ = p E sin( φ ) An Electric Dipole oriented in an Electric field has potential energy, U U = - p E = -p E cos( φ ) Electric Flux ; "flow" of E through a surface. (d A is a vector to surface) Φ Ε = E • d A (through surface) Gauss's Law expresses the fact that the source of (static) flux is charge Φ Ε = E • d A = Q encl / ε 0 Charge on a conductor at rest resides on its surface . Also for conductor Æ E inside = 0 (for static case) Use Gauss's Law to determine E field for symmetric charge distributions eg. E = σ / 2 ε 0 (for sheet) Gauss's Law easily shows E from a line of charge (instead of nasty integral) E = λ / (2 π ε 0 r) A symmetric distribution will be easier to solve for E using Gauss's Law
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Physics 51 Final Exam Study Guide(6) - Physics 51 Concept...

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