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In this Class 12 Physics topic from Chapter 1, Electric Charges and Fields, students learn how electric flux is related to the net charge enclosed by a closed surface through Gauss’s law. The topic develops the idea of Gaussian surfaces, uses symmetry to simplify electric-field calculations, and applies the law to charged spherical shells, uniformly charged spheres, infinite line charges, and plane sheets. It also helps students understand the electric field inside conductors and choose suitable surfaces for solving electrostatic problems.
Practice questions
01 A closed surface has zero net charge inside, but field is said to be outward everywhere on the surface. Why is this doubtful?
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Answer and explanation
Correct answer: A. Because outward field everywhere would give positive total flux
Explanation: Step 1: If net enclosed charge is zero, total flux must be zero. Step 2: If field is outward everywhere, every contribution is positive. Step 3: That would give positive total flux, so the statement conflicts with Gauss's law.
02 A closed surface contains net positive charge. Can the surface shape be changed so that total flux becomes zero?
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Answer and explanation
Correct answer: A. No, as long as net enclosed charge is positive total flux cannot be zero
Explanation: Step 1: Net closed flux is determined by net enclosed charge, not by surface shape. Step 2: If enclosed charge is positive, total flux remains positive. Step 3: External changes may alter local field, not total flux.
03 If net charge inside a closed surface was initially zero and then a positive charge is added inside, what change occurs in total flux?
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Answer and explanation
Correct answer: A. Total flux changes from zero to positive
Explanation: Step 1: Initially net enclosed charge was zero, so total flux was zero. Step 2: Adding a positive charge makes net enclosed charge positive. Step 3: Therefore total flux becomes positive.
04 A Gaussian surface contains a positive charge. If an equal magnitude negative charge is added inside the same surface, what happens to total flux?
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Answer and explanation
Correct answer: A. It becomes zero
Explanation: Step 1: Initially the net enclosed charge was positive. Step 2: Adding an equal magnitude negative charge makes the algebraic sum zero. Step 3: Therefore total closed flux becomes zero.
05 A Gaussian surface contains a positive charge inside and an equal magnitude negative charge outside. What is the total flux?
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Answer and explanation
Correct answer: A. Positive
Explanation: Step 1: In Gauss's law, only enclosed charge is counted. Step 2: The outside negative charge is not included in total closed flux. Step 3: Since the inside charge is positive, total flux is positive.
06 If net charge inside a closed surface is negative and a large positive charge is placed outside, what will be the sign of total flux?
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Answer and explanation
Correct answer: A. Negative
Explanation: Step 1: The outside positive charge can change field on the surface. Step 2: But total closed flux is decided by net enclosed charge. Step 3: Since enclosed charge is negative, total flux remains negative.
07 For a uniformly charged infinite line, why is electric field considered to have same magnitude everywhere on the curved surface of a Gaussian cylinder?
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Answer and explanation
Correct answer: A. Because all points on the curved surface are at the same distance from the line
Explanation: Step 1: An infinite line charge has cylindrical symmetry. Step 2: All points on the curved surface of the Gaussian cylinder are at the same radial distance from the line. Step 3: Therefore field magnitude is the same there.
08 For an infinite line charge, what is the angle between electric field and area vector on the curved surface of the cylindrical Gaussian surface?
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Answer and explanation
Correct answer: A. Zero degree
Explanation: Step 1: Field of a line charge is radial. Step 2: Area vector of the curved cylindrical surface is also radially outward. Step 3: For a positive line, both are in the same direction, so the angle is zero degree.
09 For an infinite plane sheet, why is flux through the two flat faces of the Gaussian pillbox equal?
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Answer and explanation
Correct answer: A. Because symmetry is same on both sides of the sheet
Explanation: Step 1: An infinite plane sheet has identical symmetry on both sides. Step 2: Field magnitude is same on both sides. Step 3: Hence flux through the two flat faces of the pillbox is equal.
10 If a part of a Gaussian surface is parallel to electric field, why does that part not contribute to flux?
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Answer and explanation
Correct answer: A. Because the field does not cross that part
Explanation: Step 1: Flux is related to the component of field crossing a surface. Step 2: A parallel field runs along the surface and does not pass through it. Step 3: Therefore flux through that part is zero.
11 Total flux through a closed surface is found positive, but net charge inside is stated zero. What is the most suitable comment?
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Answer and explanation
Correct answer: A. Both statements cannot be correct together
Explanation: Step 1: According to Gauss's law, total flux is proportional to net enclosed charge. Step 2: If net enclosed charge is zero, total flux must be zero. Step 3: Therefore positive total flux and zero enclosed charge are inconsistent.
12 On a closed surface, electric field is everywhere perpendicular outward and uniform in magnitude. If total surface area doubles while field remains same, what happens to total flux?
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Answer and explanation
Correct answer: A. It doubles
Explanation: Step 1: In this special case, total flux is field multiplied by total area. Step 2: Field is same and area is doubled. Step 3: Therefore total flux doubles, implying enclosed charge must also be doubled.
13 If a uniform magnitude field is everywhere perpendicular inward on a closed surface, what is the sign of net enclosed charge?
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Answer and explanation
Correct answer: A. Negative
Explanation: Step 1: Area vector of a closed surface is outward. Step 2: Inward electric field is opposite to the area vector. Step 3: Therefore total flux is negative and net enclosed charge is negative.
14 Electric field is zero everywhere on a closed surface. Can a complete electric dipole be inside it?
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Answer and explanation
Correct answer: A. It can be possible if net charge is zero and field does not reach the surface
Explanation: Step 1: If field is zero everywhere on the surface, total flux is zero. Step 2: By Gauss's law, net enclosed charge is zero. Step 3: A complete dipole has zero net charge, so Gauss's law alone does not make it impossible.
15 If Gauss's law gives zero total flux, is it always correct to take electric field as zero on the Gaussian surface while finding field?
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Answer and explanation
Correct answer: A. No, zero total flux can occur with non-zero local field
Explanation: Step 1: Total flux is an algebraic sum. Step 2: Positive and negative contributions on different parts may cancel. Step 3: Therefore zero total flux does not always mean field is zero everywhere.
16 Which is the correct distance dependence of fields from a point charge, a long line charge, and an infinite sheet using Gauss's law?
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Answer and explanation
Correct answer: A. Point inverse square, line inverse distance, sheet distance independent
Explanation: Step 1: For a point charge, spherical area grows as square of distance. Step 2: For a long line, curved cylindrical area grows with distance. Step 3: For an infinite sheet, ideal field is independent of distance.
17 In a hard Gauss's law question, what is the safest first check?
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Answer and explanation
Correct answer: A. Whether the surface is closed, what net charge is enclosed, and whether symmetry is useful
Explanation: Step 1: Gauss's law for total flux requires a closed surface. Step 2: Total flux is decided by net enclosed charge. Step 3: To find field, symmetry is needed, so check these three points first.
18 In Gauss's law, if a charge inside a closed surface is moved from the centre to near the boundary, what happens to total flux?
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Answer and explanation
Correct answer: A. It remains same
Explanation: Step 1: Gauss's law relates total flux to enclosed net charge. Step 2: Changing position of the charge does not change the enclosed charge. Step 3: Distribution may change but total flux remains same.
19 A closed surface has zero net charge inside but electric field on the surface is not zero everywhere. According to Gauss's law, what is correct?
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Answer and explanation
Correct answer: A. Net flux is zero
Explanation: Step 1: Net flux is decided only by enclosed net charge. Step 2: Since net enclosed charge is zero, net flux is zero. Step 3: Zero net flux does not mean zero field at every point.
20 A point charge is placed at the centre of a cube. What fraction of total flux passes through one face?
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Answer and explanation
Correct answer: B. One sixth
Explanation: Step 1: A cube has six equal faces. Step 2: With charge at the centre, symmetry divides total flux equally. Step 3: Each face gets one sixth of the total flux.
21 A point charge is placed at one corner of a cube. The total flux through that cube is what fraction of the full enclosed-charge flux?
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Answer and explanation
Correct answer: A. One eighth
Explanation: Step 1: Eight identical cubes can be combined to make a larger cube. Step 2: The charge becomes the centre of the larger cube and flux is shared equally. Step 3: Hence one small cube gets one eighth of the full flux.
22 A point charge is at the centre of a spherical Gaussian surface. If radius is doubled, what happens to total flux and field on the surface?
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Answer and explanation
Correct answer: A. Flux same and field one fourth
Explanation: Step 1: Total flux depends on enclosed charge, so it does not change. Step 2: Field of a point charge varies inversely as square of distance. Step 3: Doubling radius makes field one fourth.
23 Why is knowing only net flux not enough to find electric field using Gauss's law?
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Answer and explanation
Correct answer: A. Because field distribution on the surface is also needed
Explanation: Step 1: Gauss's law gives total flux. Step 2: To find field, the field must be uniform or simply directed on the surface. Step 3: Without symmetry, total flux does not directly give the field.
24 For a long uniformly charged wire, why is flux through the flat ends of a cylindrical Gaussian surface zero?
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Answer and explanation
Correct answer: A. Field is parallel to the flat ends
Explanation: Step 1: Field of a long wire is radial from the wire. Step 2: At the flat ends of the cylinder, this field lies parallel to the surface. Step 3: A field parallel to a surface gives zero flux.
25 If distance from a long line charge is made three times, what fraction of electric field remains?
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Answer and explanation
Correct answer: B. One third
Explanation: Step 1: Field of a long line charge is inversely proportional to distance. Step 2: If distance becomes three times, field becomes one third. Step 3: Do not use inverse square law for line charge.
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