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SubjectsPhysics
गाउस का नियम और इसके अनुप्रयोग
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.
Correct answer: A. At the surface
Explanation: Step 1: Inside the sphere, field increases with distance from centre. Step 2: Outside the sphere, field decreases with square of distance. Step 3: Therefore the maximum occurs at the surface.
Correct answer: A. Inversely proportional to square of distance
Explanation: Step 1: Outside the sphere, the Gaussian surface encloses the whole charge. Step 2: By spherical symmetry, outside field behaves like total charge at centre. Step 3: Hence it follows inverse-square dependence.
Correct answer: A. It becomes half
Explanation: Step 1: Inside a uniformly charged solid sphere, field is directly proportional to distance from centre. Step 2: Halving distance halves a directly proportional quantity. Step 3: So the inside field becomes half.
Correct answer: A. No net excess charge remains in the volume
Explanation: Step 1: Inside a conductor in electrostatic equilibrium, electric field is zero. Step 2: Flux through an internal Gaussian surface is zero. Step 3: Thus no net excess charge remains in the volume; it resides on the surface.
Correct answer: A. Because a tangential component would keep free charges moving along the surface
Explanation: Step 1: Conductors have free charges. Step 2: A field component along the surface would move them. Step 3: In equilibrium charges cannot keep moving, so field is normal to surface.
Correct answer: A. Surface charge density is larger there
Explanation: Step 1: Just outside a conductor, field is related to surface charge density. Step 2: Larger field means larger local surface charge density. Step 3: This explains stronger field near sharp regions.
Correct answer: A. Because surface charge density can be higher at the sharp part
Explanation: Step 1: Field near a conductor surface depends on surface charge density. Step 2: Charge can be more concentrated near sharp parts. Step 3: Hence electric field can be stronger there.
Correct answer: A. Equal magnitude negative charge
Explanation: Step 1: Field inside conducting material must remain zero. Step 2: The positive charge in cavity tends to create field in the metal. Step 3: Equal negative charge is induced on inner surface to cancel it.
Correct answer: A. Equal magnitude positive charge
Explanation: Step 1: Equal negative charge is induced on the inner surface. Step 2: The conductor was initially neutral overall. Step 3: To keep total conductor charge zero, equal positive charge appears on outer surface.
Correct answer: A. Zero
Explanation: Step 1: External charges can rearrange charges on the conductor. Step 2: In equilibrium, field inside conducting material remains zero. Step 3: With no internal source in the cavity, field inside the cavity is zero.
Correct answer: A. Positive
Explanation: Step 1: Lines leaving the surface give positive outward flux. Step 2: If leaving is greater, total flux is positive. Step 3: By Gauss's law, net enclosed charge is positive.
Correct answer: A. There is net negative charge inside
Explanation: Step 1: Entering lines contribute negative outward flux. Step 2: If they dominate, total flux is negative. Step 3: By Gauss's law, net enclosed charge is negative.
Correct answer: A. No, only total flux is zero
Explanation: Step 1: Equal entering and leaving lines make total flux zero. Step 2: Field may still exist on different parts of the surface. Step 3: Do not treat zero total flux as zero local field.
Correct answer: A. They are consistent in electrostatics
Explanation: Step 1: Both laws deal with electric fields of stationary charges. Step 2: Applying Gauss's law to a point charge gives a Coulomb-law result. Step 3: Treat them as connected, not contradictory.
Correct answer: A. Three times
Explanation: Step 1: In Gauss's law, total flux is proportional to enclosed charge. Step 2: Permittivity is unchanged, so only charge ratio matters. Step 3: Tripling enclosed charge triples the flux.
Correct answer: A. It remains unchanged
Explanation: Step 1: Total flux depends on net enclosed charge. Step 2: Rearrangement may change field distribution on the surface. Step 3: But if net enclosed charge is the same, total flux remains unchanged.
Correct answer: A. Because total flux is determined by enclosed charge, not area
Explanation: Step 1: Gauss's law connects total flux with enclosed charge. Step 2: Area change may alter local field or distribution. Step 3: But if net enclosed charge is same, total flux remains unchanged.
Correct answer: A. Only by the net charge inside
Explanation: Step 1: In Gauss's law, total flux depends only on enclosed charge. Step 2: Outside charges may change field on the surface. Step 3: But they do not change the net total flux.
Correct answer: A. No, excess charge can stay on the surface
Explanation: Step 1: In electrostatic equilibrium, field inside a conductor is zero. Step 2: This statement concerns the internal field. Step 3: A conductor may still have excess charge, but it resides on the surface.
Correct answer: A. It becomes one-fourth
Explanation: Step 1: Outside a spherical conductor, field behaves as if total charge is at the centre. Step 2: Such field follows inverse-square dependence. Step 3: Doubling distance makes field one-fourth.
Correct answer: A. Field is zero on every internal sphere
Explanation: Step 1: Inside a conductor in electrostatic equilibrium, electric field is zero. Step 2: Any internal Gaussian surface encloses no net excess charge. Step 3: Therefore field is zero at every interior point.
Correct answer: A. Net charge inside the Gaussian surface
Explanation: Step 1: Gauss's law relates total flux to enclosed charge. Step 2: Outside charges do not change total flux. Step 3: Begin the solution by finding net charge inside.
Correct answer: A. Because the surface must be closed to define enclosed charge clearly
Explanation: Step 1: Gauss's law connects total flux with a closed surface. Step 2: Only a closed surface completely encloses a volume. Step 3: Hence the enclosed-charge form is not directly used for an open surface.
Correct answer: A. Point charge, infinite line charge, and infinite plane sheet
Explanation: Step 1: A point charge gives spherical symmetry. Step 2: An infinite line charge gives cylindrical symmetry. Step 3: An infinite sheet gives plane symmetry, so a pillbox is useful.
Correct answer: A. First identify closed surface, then enclosed charge, then symmetry
Explanation: Step 1: Gauss's law is for closed surfaces, so check whether the surface is closed. Step 2: Then count only net charge inside. Step 3: Finally use symmetry to decide whether field can be found directly.
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