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Important Questions

Gauss' theorem — Important Questions

ICSE · Class 12 · Physics

107 important questions from Gauss' theorem for ICSE Class 12 Physics, with answers. Includes multiple choice, multiple correct and true false questions.

107 questions31 flashcards6 formulas & key relations5 concepts

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107 Questions·
multiple choicemultiple correcttrue false

Important Questions from Gauss' theorem

1multiple choice
3 marks

A large plane sheet has surface charge density 1.77 × 10^-11 C·m^-2. Find the electric field near the sheet and the field between two such sheets carrying equal and opposite charge densities of this magnitude.

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E near one sheet = 1.0 N·C^-1, field between opposite sheets = 2.0 N·C^-1

For one infinite plane sheet, E = σ/(2ε₀). With σ = 1.77 × 10^-11 C·m^-2, E = 1.77 × 10^-11 /(2 × 8.85 × 10^-12) = 1.0 N·C^-1. For two equal and opposite sheets, the fields add between the sheets, so E = σ/ε₀ = 2.0 N·C^-1.

2multiple choice
3 marks

A conducting sphere of radius 0.30 m carries charge 2.7 μC. Find the electric field just outside the surface and the electric field inside the sphere.

Show answer

E just outside = 2.7 × 10^5 N·C^-1, E inside = 0

Just outside a charged conductor, E = σ/ε₀ = q/(4πR²ε₀). With q = 2.7 × 10^-6 C and R = 0.30 m, E = 9.0 × 10^9 × 2.7 × 10^-6 / 0.09 = 2.7 × 10^5 N·C^-1. Inside a charged conducting sphere, the electric field is zero.

3multiple choice
3 marks

A uniformly charged non-conducting sphere has radius 0.50 m and total charge 6.0 μC. Find the electric field at r = 0.20 m from the centre.

Show answer

4.32 × 10^4 N·C^-1

Inside a uniformly charged non-conducting sphere, E = (1/4πε₀)(qr/R³). Substituting q = 6.0 × 10^-6 C, r = 0.20 m, R = 0.50 m gives E = 9.0 × 10^9 × 6.0 × 10^-6 × 0.20 / 0.125 = 4.32 × 10^4 N·C^-1.

4multiple choice
3 marks

A cube encloses a charge of 1.5 μC at any position inside it. Find the total electric flux through the cube, and then the flux if a second charge of -0.5 μC is also enclosed.

Show answer

Flux = 1.69 × 10^5 N·m²·C^-1, then 1.13 × 10^5 N·m²·C^-1

Net flux through a closed surface is Φ_E = q/ε₀. For 1.5 μC, Φ_E = 1.5 × 10^-6 / 8.85 × 10^-12 ≈ 1.69 × 10^5 N·m²·C^-1. With an added -0.5 μC, net charge becomes 1.0 μC, so flux becomes 1.0 × 10^-6 / 8.85 × 10^-12 ≈ 1.13 × 10^5 N·m²·C^-1.

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Frequently Asked Questions

What are the important topics in Gauss' theorem for ICSE Class 12 Physics?
Key topics in Gauss' theorem include Core Ideas and Basic Definitions, Gauss' Theorem and Gaussian Surface, Electric Field Due to Symmetric Charge Distributions, Important Comparisons and Sign Results. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many important questions are there in Gauss' theorem?
Super Tutor has 107 practice questions for Gauss' theorem, including multiple choice, multiple correct, true false questions. A sample with answers is on this page.

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