University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2019
Views:

254

Pages:

23
Author:

nmarie0886sck

CH22: Electric Field (E) Electric field: a region surrounded the charge through which an electric force acting on any other charge in the same region. F = Fa = kq1q2/r^2 E = Fa/qe = (kq1q2/r^2)/qe E = kq/r^2 |E| = kq/r^2 |E| = |F|/|q| = N/C The direction of electric field (E): In the same direction of the electric force acting on the point charge. [Image of an electric field line pointing away from a positive charge] Far away from the +ve charge [Image of an electric field line pointing towards a negative charge] Towards the -ve charge Electric Field Lines: Imaginary Lines represent the path of point charge in that region. [Image of electric field lines radiating outwards from a positive charge] Far away from +ve charge [Image of electric field lines converging towards a negative charge] Towards the -ve charge The electric dipole: [Image of electric field lines around an electric dipole] The neutral point of electric field # Linear Charge Distribution: Ex: Charged Ring: (uniform) dE = kdλ cosθ / r^2 Enet = ∫dE cosθ = ∫(kdλ cosθ)/r^2 = ∫(kdλ/r^2) * cosθ dθ = dl / r cosθ = z / √(r^2 + z^2) = ∫(Kλz dl) / (r^2 + z^2)^(3/2) = ∫(Kλz dl) / (R^2 + z^2)^(3/2) L = 2πR Enet = ∫(Kλz dl) / (R^2 + z^2)^(3/2) Enet = KλzL / (R^2 + z^2)^(3/2) q = λL Enet = KqZ / (R^2 + z^2)^(3/2) **Special Case:** * If z >> R (z²+R²) ≈ z² (z²+R²)^(3/2) ≈ (z²)^(3/2) ≈ z³ E_ring = KqZ / z³ = Kq/z² (point charge) * At the center of the ring, z = 0 E_ring = 0 **Ex: Charged Circular Arc:** [Image of a circular arc with a charge distribution] E = ∫dE cosθ = ∫(Kdλ cosθ)/R² = ∫(Kλ dl cosθ)/R² dl = Rdθ = ∫(KλRdθ cosθ)/R² [Image of a small segment of the arc with angle dθ] = Kλ/R ∫cosθ dθ [Image of the integration limits] = Kλ/R [sinθ] = Kλ/R [sinθ₂ - sinθ₁]