1

ΔΦ = E · ΔA = (E cos θ)ΔAΦ = ∮ E · dA[Φ] = N·m2/C

2

ε0Φ = qencε0∮ E · dA = qenck = 14πε0

3

ε0E∮dA = ε0E(4πr2) = qE = 14πε0qr2

4

: E = 0∮ E · dA = 0 ⇒ qenc = 0

5

: E = σ2ε0: E = σε0: E = λ2πε0r

6

r > R: E = 14πε0qr2: E = 0: E = q4πε0R3r

7

V = −W∞q0 = Uq0U = qVΔK = −ΔU = −qΔV1 V = 1 J/C,  1 N/C = 1 V/m1 eV = 1.602 × 10−19 J

8

Vf − Vi = −∫if E · dsΔV = −EΔxEs = −∂V∂sE = −∇V

9

V = 14πε0qrV = ΣVi = 14πε0ΣqiriV ≈ 14πε0p cos θr2Ez = 12πε0pz3

10

dV = 14πε0dqrVrod = λ4πε0 lnL + L2 + d2dVdisk = σ2ε0(z2 + R2 − z)Ez = σ2ε0(1 − zz2 + R2)

11

U = 14πε0q1q2rU = 14πε0(q1q2r12 + q1q3r13 + q2q3r23)

12

Vf − Vi = 0q1r1 = q2r2σ1 : σ2 = 1r1 : 1r2

E(x, y, z) = (Ex, Ey, Ez)

V(x, y, z)