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10 days ago

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The electric field in a particular space is = (x + 3.6) N/C with x in meters. Consider a cylindrical Gaussian surface of radius

16 cm that is coaxial with the x axis. One end of the cylinder is at x = 0. (a) What is the magnitude of the electric flux through the other end of the cylinder at x = 3.7 m? (b) What net charge is enclosed within the cylinder?

1 answer:

Maru [2.3K]10 days ago

6 0

Answer:

a) Ф = 0.016 N / C m, b) q_{int} = 0.14 10⁻¹² C

Explanation:

a) For this scenario, we rely on Gauss's law

Ф = E.ds = $q_{int}$ /ε₀

As the field points in the x direction, there is no flux through the cylinder walls.

Ф = E A

The area of a circle is

A = π r

Ф = E π r

Ф = (x- 3.6) r

Now, let's compute

Ф = (3.7 -3.6) 0.16

Ф = 0.016 N / C m

b) Using Gauss's law, we have

q_{int} = Ф ε₀

Where the flow is present on both sides, at the face corresponding to x = 0, the flow is zero

q_{int} = 0.016 8.85 10⁻¹²

q_{int} = 0.14 10⁻¹² C

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