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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 part of a Gaussian surface has electric field opposite to the outward normal. What is the flux through that part?
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Answer and explanation
Correct answer: A. Negative
Explanation: Step 1: For a closed surface, outward normal is taken positive. Step 2: If field is opposite to it, field lines are entering. Step 3: Therefore flux through that part is negative.
02 On a surface, electric field has only tangential component and no normal component. What is the flux through that surface?
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Answer and explanation
Correct answer: A. Zero
Explanation: Step 1: Only the normal component crossing the surface contributes to flux. Step 2: Tangential component runs along the surface and does not pass through it. Step 3: Therefore flux is zero.
03 Just outside a conductor, field is normal to the surface. Which conductor property does this support along with Gauss's law?
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Answer and explanation
Correct answer: A. No tangential field remains at the surface in equilibrium
Explanation: Step 1: In electrostatic equilibrium, free charges in a conductor should not move. Step 2: A tangential field would make them move. Step 3: Therefore outside field at the surface remains normal.
04 What is common between outside field of a uniformly charged conducting sphere and a uniformly charged non-conducting solid sphere?
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Answer and explanation
Correct answer: A. Both behave outside like total charge at the centre
Explanation: Step 1: In both cases, an outside Gaussian surface encloses the whole charge. Step 2: Due to spherical symmetry, outside result is like a point charge at the centre. Step 3: The main difference appears inside the sphere.
05 What is the main difference between inside field of a conducting sphere and a uniformly charged solid non-conducting sphere?
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Answer and explanation
Correct answer: A. In conductor field is zero inside, in solid non-conductor it can increase from centre
Explanation: Step 1: In a conductor, charge stays on surface and field inside is zero. Step 2: In a uniformly charged solid non-conductor, charge is spread through volume. Step 3: Hence inside field can increase from the centre.
06 A Gaussian surface encloses no charge but external charges create field on it. What is the net flux?
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Answer and explanation
Correct answer: A. Zero
Explanation: Step 1: In Gauss's law, net flux is decided by enclosed net charge. Step 2: The enclosed charge is zero. Step 3: Lines from outside charges enter and leave equally, so net flux is zero.
07 If net flux through a closed surface is positive, what can be said in terms of field lines?
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Answer and explanation
Correct answer: A. More lines leave than enter
Explanation: Step 1: Outward direction is taken positive. Step 2: Positive net flux means outgoing contribution is greater. Step 3: This indicates positive net charge inside the closed surface.
08 If net flux through a closed surface is negative, which explanation is correct?
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Answer and explanation
Correct answer: A. Field lines are net entering the surface
Explanation: Step 1: For a closed surface, outward direction is positive. Step 2: Negative flux means inward contribution is greater. Step 3: This indicates negative net charge inside.
09 A point charge is outside a Gaussian surface. It creates field on the surface, yet why is net flux zero?
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Answer and explanation
Correct answer: A. Lines both enter and leave the surface
Explanation: Step 1: Field lines of an external charge can cross the closed surface. Step 2: Lines that enter also leave it. Step 3: Therefore entry and exit cancel and net flux is zero.
10 When can changing the Gaussian surface still give the same electric field result?
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Answer and explanation
Correct answer: A. When the new surface also uses the same symmetry correctly
Explanation: Step 1: Gaussian surface is a calculation tool. Step 2: If another surface also captures the symmetry correctly, the same physical field is obtained. Step 3: While changing surface, do not disturb enclosed charge and symmetry logic.
11 For a symmetric charge distribution, a Gaussian surface is chosen so that field is normal to the surface. What is the advantage?
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Answer and explanation
Correct answer: A. Flux calculation becomes simple
Explanation: Step 1: For normal field, the full crossing component contributes. Step 2: If magnitude is also simple, total flux is easy to calculate. Step 3: This is why a proper Gaussian surface is chosen.
12 If a part of a Gaussian surface has zero electric field, what is the flux through that part?
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Answer and explanation
Correct answer: A. Zero
Explanation: Step 1: Flux is related to electric field and area. Step 2: If field itself is zero, no electric effect crosses the surface. Step 3: Therefore flux through that part is zero.
13 A complete electric dipole is enclosed by a closed surface. What is the relation between net flux and enclosed net charge?
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Answer and explanation
Correct answer: A. Both are zero
Explanation: Step 1: A dipole has equal positive and negative charges. Step 2: When the whole dipole is enclosed, net enclosed charge is zero. Step 3: By Gauss's law, net flux is also zero.
14 If a closed surface encloses only the negative charge of a dipole and the positive charge is outside, what is the net flux?
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Answer and explanation
Correct answer: A. Negative
Explanation: Step 1: In Gauss's law, only the charge inside is counted. Step 2: The surface encloses negative charge while positive charge is outside. Step 3: Therefore net flux is negative.
15 If a closed surface encloses only the positive charge of a dipole and the negative charge is outside, what is the net flux?
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Answer and explanation
Correct answer: A. Positive
Explanation: Step 1: Net flux through a closed surface is decided by net charge inside. Step 2: Only positive charge is inside, so enclosed net charge is positive. Step 3: Hence net flux is positive.
16 According to Gauss's law, total flux does not depend on which factor?
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Answer and explanation
Correct answer: A. Charges placed outside the closed surface
Explanation: Step 1: Enclosed net charge is the main factor for net flux. Step 2: Outside charges can change field on the surface but not total flux. Step 3: Do not add outside charges to enclosed charge.
17 In a difficult Gauss's law question, what is the safest first step?
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Answer and explanation
Correct answer: A. Identify the closed surface and its net enclosed charge
Explanation: Step 1: Gauss's law connects net flux with enclosed charge. Step 2: So first identify the closed surface and which charges are inside it. Step 3: Then use symmetry and calculate field if possible.
18 In Gauss's law, total flux through a closed surface is zero, but electric field is non-zero at many points on the surface. What is the most correct meaning?
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Answer and explanation
Correct answer: A. Net enclosed charge is zero, field need not be zero everywhere
Explanation: Step 1: Gauss's law relates total flux only to net enclosed charge. Step 2: When net charge is zero, positive and negative flux contributions may cancel. Step 3: Do not confuse zero total flux with zero field everywhere.
19 A Gaussian sphere centered on a point charge has its radius made three times. What happens to total flux?
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Answer and explanation
Correct answer: A. It remains unchanged
Explanation: Step 1: Total flux depends on enclosed charge. Step 2: Changing radius still keeps the same point charge enclosed. Step 3: Therefore total flux does not change, although field on the surface changes.
20 For the same point charge, if the radius of the Gaussian sphere is made three times, what happens to the electric field magnitude on the surface?
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Answer and explanation
Correct answer: A. One-ninth of the earlier value
Explanation: Step 1: Field of a point charge varies inversely with square of distance. Step 2: Tripling radius makes square of distance nine times. Step 3: Hence field on the surface becomes one-ninth.
21 When radius of a Gaussian sphere is tripled, field decreases. Why does total flux still remain same?
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Answer and explanation
Correct answer: A. Because field decreases but surface area increases and enclosed charge is same
Explanation: Step 1: Field due to a point charge decreases with distance. Step 2: At the same time, area of the sphere increases with square of distance. Step 3: These effects keep total flux fixed according to enclosed charge.
22 A positive charge is inside a closed surface and an equal negative charge is outside. What is the total outward flux?
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Answer and explanation
Correct answer: A. Positive, depending only on the inside charge
Explanation: Step 1: In Gauss's law, only enclosed charge decides total flux. Step 2: The outside negative charge may create field on the surface, but its net flux contribution is zero. Step 3: Hence total outward flux remains positive.
23 If total outward flux through a closed surface is negative, which conclusion about net enclosed charge is correct?
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Answer and explanation
Correct answer: A. Net enclosed charge is negative
Explanation: Step 1: The sign of outward flux is linked to the sign of net enclosed charge. Step 2: Negative total flux means net field lines are inward. Step 3: Therefore net enclosed charge is negative.
24 A closed surface encloses three positive charges and two negative charges of equal magnitude. What is the sign of total flux?
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Answer and explanation
Correct answer: A. Positive
Explanation: Step 1: Total flux depends on net enclosed charge. Step 2: Three positive and two equal negative charges leave one positive charge as net. Step 3: Therefore total outward flux is positive.
25 A closed surface encloses two positive charges and five negative charges of equal magnitude. What will be the total flux?
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Answer and explanation
Correct answer: A. Negative
Explanation: Step 1: In Gauss's law, the sign of net enclosed charge gives the sign of total flux. Step 2: Two positive and five negative charges give net negative charge. Step 3: Hence total outward flux is negative.
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