Useful Formulae in Advanced Level Physics v = w 2r r 2 A1. a= A2. a = w 2c simple harmonic motion A3. L = Iw angular momentum of a rigid body A4. .T = dL dt torque on a rotating body A5. E= 1 2 Iw 2 energy stored in a rotating body B1. v= T m velocity of transverse wave motion in a stretched string B2. v= E r velocity of longitudinal wave motion in a solid B3. n = tan q p B4. d= B5. d sin q = nl diffraction grating equation B6. u - u0 f '= f ( ) u - us Doppler frequency B7. 10 log10 ( C1. F= Gm1 m2 r2 Newton’s law of gravitation C2. V = GM r gravitational potential C3. r3 / T2 = constant C4. E= Q 4pe 0 r 2 electric field due to a point charge C5. V = Q 4pe 0 r electric potential due a point charge lD a centripetal acceleration refractive index and polarizing angle fringe width in double-slit interference I2 ) I1 definition of the decibel Kepler’s third law 1 C6. E= V d electric field between parallel plates (numerically) C7. C= Q e0 A = V d capacitance of a parallel-plate capacitor C8. Q = Qo e -t / RC decay of charge with time when a capacitor discharges C9. Q = Qo (1 - e -t / RC ) rise of charge with time when charging a capacitor C10. E= C11. I = nAuQ C12. R= C13. F = BQu sin q force on a moving charge in a magnetic field C14. F = BI ﺎsin q force on a current carrying a conductor in a magnetic field C15. V= BI nQt Hall voltage C16. B= m0I 2pr magnetic field inside a long straight wire C17. B= m 0 NI l magnetic field inside long solenoid C18. F= m 0 I1 I 2 2pr force per unit length between long parallel straight current 1 CV 2 2 rl A energy stored in a capacitor general current flow equation resistance and resistivity carrying conductors C19. T = BAN sin f torque on a rectangular current carrying coil in a uniform magnetic field C20. E = BANw sin wt simple generator e.m.f. C21. Vs N » s Vr N r ratio of secondary voltage to primary voltage in a transformer C22. E = - LdI / dt e.m.f. induced in an inductor C23. E= 1 2 LI 2 energy stored in an inductor C24. X L = wL reactance of an inductor 2 1 wC C25. XC = C26. P = IVCOS q C27. DVout / DVin = - b reactance of a capacitor power in an a.c. circuit RL RB voltage gain of transistor amplifier in the common emitter configuration C28. Vo = Ao (V+ - V- ) C29. A=- C30. A = 1+ D1. pV = nRT = NkT D2. pV = 1 Nmc 2 3 kinetic theory equation D3. Ek = 3RT 3 = kT 2N A 2 molecular kinetic energy D4. E= F x / A L macroscopic definition of Young modulus D5. E= 1 Fx 2 energy stored in stretching D6. F =- D7. E = .k / r Rf Ri Rf Ri dU dr 1 2 rv + rgh 2 = constant output voltage of op amp (open-loop) gain of inverting amplifier gain of non-inverting amplifier equation of state for an ideal gas relationship between force and potential energy microscopic interpretation of Young modulus P+ Bernoulli’s equation D9. ∆U = Q + W first law of thermodynamics D10. En = - D11. N = N o e - kt D12. t1 = D8. 2 13.6 eV n2 ln 2 k energy level equation for hydrogen atom law of radioactive decay half-life and decay constant 3 D13. 1 mu m2 = hv - f 2 Einstein’s photoelectric equation D14. E = mc2 mass-energy relationship Downloaded from : Gcecompilation.com 4