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vodomira
9 days ago
5

A spherically symmetric charge distribution has a charge density given by ρ = a/r , where a is constant. Find the electric field

within the charge distribution as a function of r. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0. Consider that a is positive.)
Physics
2 answers:
inna [2.2K]9 days ago
6 0

Response:

E = a/2ε۪

Explanation:

A charge distribution that is spherically symmetric has a density expressed as ρ = a/r, where a is a constant. Determine the electric field inside the charge distribution in terms of r. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr²dr. (Use as necessary: a, r, and ε0, with a being positive.)

The charge on a spherical shell is represented as

dQ = (charge density) × (surface area) × dr

dQ = ρ(r)4πr²dr

By integrating both sides, we derive

∫ dQ = ∫ (a/r)4πr²dr

∫ dQ = 4πa ∫ rdr

Considering the limits from r to 0

Q(r) = 2πar² - 2πa0²

Q = 2πar² (= total charge encompassed by a spherical surface with radius r)

(Flux through surface) = (charge included by surface)/ε۪

Gauss's law

(Surface area of the sphere) × E = Q/ε۪

4πr²E = 2πar²/ε۪

E = a/2ε۪

Yuliya22 [2.4K]9 days ago
3 0
The infinitesimal charge dQ on a layer with thickness dr is expressed as

dQ = (charge density) × (surface area) × dr

dQ = ρ(r)4πr²dr

∫ dQ = ∫ (a/r)4πr²dr

∫ dQ = 4πa ∫ rdr

Q(r) = 2πar² - 2πa0²

Q = 2πar² (= total charge confined within a spherical surface of radius r)

According to Gauss's Law:

(Flux through surface) = (charge enclosed by surface)/ε۪

(Surface area of sphere) × E = Q/ε۪

4πr²E = 2πar²/ε۪

<span>E = a/2ε۪


I trust my response has been helpful. Thank you for your question! We hope to assist with your future inquiries. Have a great day!

</span>
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kicyunya [2264]

Answer:

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According to the question, the information provided is:

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h = 3.57 m

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