Comprehensive Formula sheet - PHYS 272 1 = k = 9 × 10⁹ 4 περ N. m² C² C² le 1.6 x 10-19 C €8.85 x 10-12 μο T. m² 1 x 10-7 N. m² 4 π C m/s 1. The electric field of a point charge q: 2. The electric force on a charge q: F = qE 3. The electric field at a location on the dipole axis: 4 5. 6. 1 2qsr Eaxis ¯ 4π €。 (r−³)² (r+³)² The electric field at a location perpendicular to the dipole axis: 1 q s E₁ = 4 ΠΕ0 · [r² + (²)²] ³/² 3/2 If r >> s, Eaxis 4 περ 1 2qs r3 1 qs If rs, E₁ 4π € г³ For a location on the perpendicular axis of a uniformly charged rod and at a distance r from the center of the rod, the electric field: 1 9 Erod = If r >> L, Erod 4 περ 2+ r () 1 q 4 π Є。 r² 1 2q/L If Lr, Erod 4 περ I The electric field along the axis of a uniformly charged ring, a distance r from the center of the ring: 1 Ering = qr 4πЄo (R2+2)3/2 1 q If r >> R, Ering 4περ μ 1 q 7. The electric potential due to a point charge q: V = 8. 9. The change in the electric potential for a uniform electric field: AV = -E. A The change in the electric potential for non-uniform electric field: AV = -SE. di 10. The change in electric potential energy: AU = q AV 11. The magnetic field of a moving point charge: B = Ho qvxr 4πT 2 12. The magnetic field due to a current-carrying straight wire: 1 If R >> r, Ering qr 4π €。 R³ Ho Bwire = IL Но 21 If L≫r (long wire) Bwire = 4π r√r² + (L/2)² 4π r 13. The magnetic field of a current-carrying coil (A = πR²): μο 2IAN Ho 2IAN B If r> R B coil 4π (r² + R2)3/2' coil 4 π r3 B center 14. The magnetic field inside a long solenoid: HONI B 15. The magnetic field of a bar magnet: Bmagnet 16. Ohms' Law: V = IR 17. Electric Power: P = IV 18. Magnetic force on a moving charge: =qx 19. Magnetic force on a current carrying wire due to a uniform magnetic field: F = ILXB 20. Electric flux for a uniform electric field: * = Ē.ĥ A 21. Electric flux for any electric field: = √ Ē.ñ dA 22. Gauss's Law: 6 E. ñ dA = Σinside Eo 23. Magnetic flux for a uniform magnetic field: += B.nz. 24. Magnetic flux for any magnetic field: += √ B.ñ dA 25. Ampere's Law: $ B. dỉ = HoΣlinside 26. Faraday's Law: emf = - A mag At 27. The frequency of the wave: f = 1/T 28. The angular frequency: v = 2nf 29. The speed of the wave: v = λf 30. Index of refraction: n = c/v 31. Law of refraction (Snell's Law): n₁sine₁ = n₂sine₂ = Ho 2πIN 4TT R Two very long parallel straight wires of length L, are a distance d = 4 [cm] apart. The upper wire carries a conventional current I₁ = 9 [A] and the lower wire carries a conventional current I2 = 5 [A] in the same direction. L 12 1. Calculate the magnetic field B due to wire 1 at any point of wire 2. Bby 1 on 2 =< > [T] 2. Calculate the magnetic field B due to wire 2 at any point of wire 1. Bby 2 on 1 =< > [T] 3. Calculate the magnetic force per unit length due to wire 1 on wire 2. Fby 1 m 2 =< L [N/m] 4. Calculate the magnetic force per unit length due to wire 2 on wire 1. Fby 2m 1 =< L [N/m]