Unit 8: Magnetism (v1) AP Physics Memorization Material Equations 1. FB = qv × B magnetic force on a moving charged particle (Lorentz Force) 2. FB = qvBsin θ = qv⊥ B magnitude of magnetic force on a moving charged particle, where θ is the angle between v and B 3. F= 4. mv 2 r 2π r v= T 5. FB = ∫ I d × B 6. FB = i L × B 7. FB = IBsin θ force needed to hold an object in circular motion µ o I d × r µ o i ds × r̂ 8. dB = = 4π r 3 4π r 2 µI 9. B = o 2π r 10. ∫ B ⋅ d = µo I or ∫ B ⋅ ds = µo ienc 11. B = µ o nI 12. ΦB = φm = ∫ B ⋅ dA 13. ΦB = φm = B ⋅ A = BAcosθ dφm = E ⋅ ds ∫ dt dΦ m 15. E = −N dt 14. E = − ΦB i 2 18. L = µ on A 17. L = N 20. τ L = L 23. U L = 24. ω = magnetic flux through an area magnetic flux through an area when B is uniform. θ is the angle between B and the way A “faces” Change in flux induces a circular electric field (Faraday’s Law). One loop around circular electric field yields an emf. induced emf by a change in a flux through N loops of wire inductance based on a coil’s geometry back-emf for an inductor time constant for inductor R ( integrating B around a loop yields the current passing through the loop (Ampere’s Law) magnetic field created by a solenoid definition of inductance di dt E −t τ 1− e L R −t τ 22. i = io e L 21. i = magnetic field created by a long straight current carrying wire induced emf in a conductor sweeping perpendicularly through a magnetic field 16. E = Bv 19. E = −L relationship between circular motion, radius and period magnetic force on a current carrying wire, where B changes or direction of wire changes magnetic force on a current carrying wire, where wire is straight and B is constant throughout wire’s length magnitude of the magnetic force on a straight current carrying wire with constant B , where θ is the angle between B and I . element of magnetic field created by an element of a current-carrying wire. Both the AP and the textbook versions. (Biot-Savart Law) ) 1 2 LI 2 1 LC 25. q = Qcos (ω t + φ ) Current rises to E/R after an emf is introduced to a L-R series circuit Current decays to zero if the emf is removed from a L-R series circuit energy stored in an inductor angular frequency for an oscillating LC circuit charge as a function of time on a capacitor in an LC circuit, with Q as the amplitude, ω as the angular frequency, and φ as a phase change. Symbols A= B= E= F= i=I= L= = L= µo = n= N= q= r= r̂ = r= T= τL = v= φm = Φ M = Φ B = Units area enclosed by a loop of wire magnetic field electro-motive force force current length inductance permeability of free space loop or coil density number of loops charge radius of circle unit vector in the direction of r position vector period time constant velocity of a charged particle magnetic flux meters2 Teslas volts Newtons Amperes meters Henry Tesla-meters/amp 1/meters none Coulombs meters meters meters seconds seconds meters/second webers m2 T V N A m H T m/A m–1 C m m m s s m/s Wb Complex Units T= N N ⋅s = A⋅m C⋅m N=kg m s2 J=kg Wb = T·m2 C A= s V= m2 s2 J Wb = C s H= Tm 2 Wb = A A Right Hand Rules Rule Name 1. Force on particle 2. Force on current 3. F on charges along wire Rule Name 4. Current 5. Ampere’s Law 6. Lenz’s Law 7. Solenoid Equation # 1 5, 6 16 Equation # 8,9 10 14, 15 11 straight fingers (cause) v of + particle I (+ flow) v (⊥ to wire) bent fingers (cause) B-field B-field B-field thumb (result) force on particle force on wire push on + (+ end of voltage) Thumb (cause) I (+ flow) + direction of I inside loop opposite to dΦB dt Fingers Wrap (result) B-field B-field around loop E-field or emf around loop (result) B-field inside solenoid (cause) I wrapping around solenoid