27: Problem 27.16

INTRO:
None

Figure 1	Figure 2

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PART A:

What is the net electric flux through the cylinder (a) shown in (Figure 1) ?
Express your answer in terms of the variables E, R, and the constant π.

SOLUTION:

Gauss's Law: Φ_E=∫E⋅dA

∫E = (E_IN - E_OUT)

Area: A = πr² = π(1/2 ⋅ 2R)²        normal vector = i^

A = πR²i^

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∫E = (Ei^ - Ei^) = 0

Φ_E= [(Ei^ - Ei^) = 0]⋅(πR²)i^

Φ_E = 0

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PART B:

What is the net electric flux through the cylinder (b) shown in (Figure 2) ?
Express your answer in terms of the variables E, R, and the constant π.

SOLUTION:
Gauss's Law: Φ_E=∫E⋅dA

∫E = (E_IN - E_OUT)

Area: A = πr² = π(1/2 ⋅ 2R)²        normal vector = i^

A = πR²i^
​

∫E = (Ei^ - (-Ei^)) = 2Ei^

Φ_E= (2Ei^)⋅(πR²)i^

Φ_E = 2EπR²