4300372

26 de março de 2015  P 1

Eletromagnetismo

Nome:  n\underline{o} USP

1– (4.0)

• (1.0) a)

• (1.0) b)

• (0.5) c)

• (0.5) d)

• (1.0) e)

2– (3.0)

• (1.0) a)

• (1.0) b)

• (0.5) c)

• (0.5) d)

• (1.0) e)

3– (3.0) • (1.0) a)

• (1.0) b)

• (1.0) c)

• (0.5) d) a distância entre o máximo de segunda ordem e o máximo central.

Formulário

D⃗ = ϵ_{o} E⃗ + P⃗  B⃗ = μ_{o} H⃗ + M⃗  D⃗ = ϵ E⃗  B⃗ = μ H⃗
∇.D⃗ = ρ  ∇ × H⃗ = J⃗ + \frac{∂D⃗}{∂t}  σ_{p} = P⃗ .n⃗

∇.D⃗ = \frac{∂D_{x}}{∂x} + \frac{∂D_{y}}{∂y} + \frac{∂D_{z}}{∂z} ∇.D⃗ = \frac{1}{r} \frac{∂}{∂r} (rD_{r}) + \frac{1}{r} \frac{∂D_{ϕ}}{∂ϕ} + \frac{∂D_{z}}{∂z} (coord. cilíndricas) ∇D⃗ = \frac{1}{r^{2}} \frac{∂}{∂r} (r^{2}D_{r}) + \frac{1}{rsenθ} \frac{∂}{∂θ} (senθD_{θ}) + \frac{1}{rsenθ} \frac{∂D_{ϕ}}{∂ϕ} ∇ × H⃗ = (\frac{∂H_{z}}{∂y} − \frac{∂H_{y}}{∂z})i⃗ + (\frac{∂H_{x}}{∂z} − \frac{∂H_{z}}{∂x}) j⃗ + (\frac{∂H_{y}}{∂x} − \frac{∂H_{x}}{∂y}) k⃗ ∇ × H⃗ = (\frac{1}{r} \frac{∂H_{z}}{∂ϕ} − \frac{∂H_{ϕ}}{∂z})a⃗_{r} + (\frac{∂H_{r}}{∂z} − \frac{∂H_{z}}{∂r}) a⃗_{ϕ} + \frac{1}{r} (\frac{∂(rH_{ϕ})}{∂r} − \frac{∂H_{r}}{∂ϕ}) a⃗_{z} (coord. cilíndricas)

k⃗ × E⃗ = ωB⃗  S⃗ = \frac{1}{μ} E⃗ × B⃗  P = f_{a} \frac{<S>}{c} + 2f_{r} \frac{<S>}{c}  E_{o} = cB_{o}
< p > = f_{a} \frac{<U>}{c} + 2 f_{r} \frac{<U>}{c}  P_{ot} = ∫ S⃗.d⃗A  I = I_{o} cos^{2} θ  c = 3 × 10^{8} m/s
D_{1n} = D_{2n}  E_{1t} = E_{2t}  B_{1n} = B_{2n}  H_{1t} = H_{2t}  tan θ_{i}_{B} = \frac{n_{t}}{n_{i}}  θ_{i} + θ_{t} = \frac{π}{2}

Interferência mλ = d sen θ (m + \frac{1}{2})λ = d sen θ mλ = a sen θ (m + \frac{1}{2})λ = a sen θ sen θ = 1.22 \frac{λ}{a} λ_{n} = \frac{λ}{n}

mλ = a sen θ  (m + \frac{1}{2})λ = a sen θ  sen θ = 1.22 \frac{λ}{a}
I = I_{o} (\frac{sen \frac{β}{2}}{\frac{β}{2}} )^{2} (\frac{sen \frac{Nϕ}{2}}{sen \frac{ϕ}{2}} )^{2}  ϕ = \frac{2π}{λ} d sen θ  β = \frac{2π}{λ} a sen θ  R = \frac{λ_{m}}{λ_{2} − λ_{1}} = \frac{λ_{m}}{Δλ}  R = m N

Película 2nt = (m + \frac{1}{2}) λ m = 0, 1, 2, ...... 2nt = m λ m = 0, 1, 2, ...... t cosθ_{t} = (2m + 1)\frac{λ_{t}}{4} m = 0, 1, 2, ...... t cosθ_{t} = m \frac{λ_{t}}{2} m = 0, 1, 2, ...... Difração sen θ = 1.22 \frac{λ}{a} mλ = a sen θ (m + \frac{1}{2})λ = a sen θ

I = I_{o} (\frac{sen \frac{πa sen θ}{λ}}{\frac{πa sen θ}{λ}})^{2} Rêde de difração mλ = d sen θ (m + \frac{1}{2})λ = d sen θ

I = I_{o} cos^{2} (\frac{πd sen θ}{λ})(\frac{sen \frac{πa sen θ}{λ}}{\frac{πa sen θ}{λ}})^{2}

R = \frac{λ_{m}}{λ_{2} − λ_{1}} = \frac{λ_{m}}{Δλ} R = m N