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MCQEasyJEE 2023Gauss's Law Applications

JEE Physics 2023 Question with Solution

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius RR, with distance rr from the center OO is represented by:

Four candidate graphs of electric field E versus distance r for a uniformly charged solid sphere, along with a sphere diagram showing center O and radius R.
  • A

    (1)(1)

  • B

    (2)(2)

  • C

    (3)(3)

  • D

    (4)(4)

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: A uniformly charged insulating solid sphere of radius RR. We need the graph of electric field EE versus distance rr from the center OO.

Find: Which graph correctly represents the variation of EE with rr.

Step 1: Analyze the electric field inside and outside the sphere.

  • Inside the sphere (r<R)(r < R): Electric field increases linearly with rr due to the uniformly distributed charge.
  • Outside the sphere (r≥R)(r \ge R): Electric field decreases as 1r2\frac{1}{r^2}, behaving like a point charge at the center.

Step 2: Draw the graph.

  • Combine the two observations to get the correct graph for the electric field variation.

Conclusion: The correct graph is represented by option (4)(4). Therefore, the correct option is D.

Common mistakes

  • Assuming the electric field inside the uniformly charged solid sphere is constant. This is wrong because the enclosed charge increases with r3r^3, giving E∝rE \propto r inside. Use a linearly increasing graph from the center to r=Rr = R instead.

  • Confusing a solid insulating sphere with a conducting sphere. For a conductor, the electric field inside is zero, but for a uniformly charged insulating sphere it is not zero except at the center. Identify the material type before choosing the graph.

  • Choosing a graph that continues to increase beyond r=Rr = R. This is wrong because outside the sphere the field behaves like that of a point charge and decreases as 1r2\frac{1}{r^2}. After reaching its maximum at r=Rr = R, the graph must fall.

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