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The electric field inside a sphere which carries a charge density proportional to the distance from the origin ρ = α r (α is a constant is)
  • a)
    α r2/3 ε0
  • b)
    α r2/4ε0
  • c)
    α r3/4ε0
  • d)
    α r3/3ε0
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The electric field inside a sphere which carries a charge density prop...
Explanation:

Charge Density:
- The charge density ρ inside the sphere is given by ρ = αr, where α is a constant.

Gauss's Law:
- According to Gauss's Law, the electric field inside a uniformly charged sphere is given by E = (ρr)/(3ε₀) for r ≤ R.

Electric Field Calculation:
- Substituting the given charge density ρ = αr into Gauss's Law, we get E = (αr * r)/(3ε₀) = αr^2/(3ε₀).
- Therefore, the electric field inside the sphere is proportional to r^2.

Comparing with Options:
- The correct option is b) αr^2/4ε₀, as the electric field is directly proportional to r^2 according to Gauss's Law.
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The electric field inside a sphere which carries a charge density proportional to the distance from the origin ρ = α r (α is a constant is)a)α r2/3 ε0b)α r2/4ε0c)α r3/4ε0d)α r3/3ε0Correct answer is option 'B'. Can you explain this answer?
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