Gauss's Law and its Applications

Correct answer: A. Same total charge placed at the centre

Explanation: Step 1: Excess charge of a conducting sphere resides on the surface. Step 2: For outside points, spherical symmetry exists. Step 3: Thus outside field is like that of total charge placed at the centre.

Correct answer: A. It increases with distance from centre

Explanation: Step 1: In an insulating sphere, charge may be distributed through volume. Step 2: Enclosed charge inside a smaller Gaussian sphere increases with cube of radius. Step 3: As a result, inside field increases with distance from centre.

Correct answer: A. Zero inside conductor, may vary with distance inside insulator

Explanation: Step 1: In a conductor, excess charge moves to the surface. Step 2: Hence inside conductor field is zero in electrostatic condition. Step 3: In an insulator, charge can remain in volume, so inside field may vary.

Correct answer: A. It becomes half

Explanation: Step 1: Field of a long charged line is inversely proportional to distance. Step 2: Doubling distance makes field half. Step 3: Do not confuse it with square dependence of point charge.

Correct answer: A. One fourth

Explanation: Step 1: Field of a point charge is inversely proportional to square of distance. Step 2: When distance is doubled, square factor becomes four. Step 3: Therefore field becomes one fourth.

Correct answer: A. It remains unchanged

Explanation: Step 1: Field of an infinite plane sheet is independent of distance. Step 2: Even if distance doubles, field magnitude does not change in the ideal case. Step 3: This result is based on symmetry of an infinite sheet.

Correct answer: A. Point charge inverse square, line charge inverse distance, infinite sheet distance independent

Explanation: Step 1: For a point charge, spherical area grows as square of distance. Step 2: For a line charge, cylindrical area grows with distance. Step 3: For an infinite sheet, field comes independent of distance.

Correct answer: A. Electric field times total area

Explanation: Step 1: Outward perpendicular field crosses every small part directly. Step 2: Since magnitude is same everywhere, total flux is field multiplied by total area. Step 3: This is simple only when direction and magnitude are uniform.

Correct answer: A. It can be zero

Explanation: Step 1: Outward field gives positive flux. Step 2: Inward field gives negative flux. Step 3: If the two contributions are equal, total flux can be zero.

Correct answer: A. When symmetry makes magnitude same everywhere

Explanation: Step 1: To take field out of flux calculation, its magnitude must be same on the surface. Step 2: This usually comes from symmetry. Step 3: Without symmetry, assuming this can be a mistake.

Correct answer: A. First identify closed surface, enclosed charge, and symmetry

Explanation: Step 1: A closed surface is essential in Gauss's law. Step 2: Total flux is decided by net enclosed charge. Step 3: To find field, use symmetry and choose the correct Gaussian surface.

Correct answer: A. Net charge enclosed inside the surface

Explanation: Step 1: Gauss's law connects total flux through a closed surface with enclosed net charge. Step 2: Shape or colour of the surface does not directly decide net flux. Step 3: In such questions, first check the net charge inside the closed surface.

Correct answer: B. It becomes double

Explanation: Step 1: According to Gauss's law, total flux is proportional to enclosed charge. Step 2: If enclosed charge doubles, flux also doubles. Step 3: In ratio questions, remember the direct relation between enclosed charge and flux.

Correct answer: C. Positive

Explanation: Step 1: First add the charges enclosed by the closed surface. Step 2: Three coulomb positive and one coulomb negative give a net positive charge. Step 3: Positive net charge gives positive net flux.

Correct answer: D. Zero

Explanation: Step 1: In Gauss's law, net flux is decided only by net enclosed charge. Step 2: An outside charge can create field on the surface, but its net flux contribution is zero. Step 3: If no charge is inside, write net flux as zero.

Correct answer: A. Because symmetry allows electric field to be treated simply

Explanation: Step 1: Gauss's law gives total flux. Step 2: To find electric field, the field magnitude or direction should often be simple on the Gaussian surface. Step 3: So choosing a surface using symmetry is very useful in exams.

Correct answer: B. Because field is radial and same at equal distance everywhere

Explanation: Step 1: A point charge has spherical symmetry around it. Step 2: With the charge at the centre, every point of the sphere is at the same distance and field is normal to the surface. Step 3: For point charge, remember spherical Gaussian surface.

Correct answer: A. The wire has cylindrical symmetry

Explanation: Step 1: Field of a long straight wire is radial from the wire. Step 2: On the curved part of a cylindrical surface, flux can be calculated simply. Step 3: Cylindrical symmetry is most useful for line charge.

Correct answer: B. Because equal flux on both sides can be added simply

Explanation: Step 1: For an infinite plane sheet, field on both sides is equal in magnitude and normal to the sheet. Step 2: A small cylindrical pillbox gives flux through the two flat faces. Step 3: For plane sheet, add contributions from both sides carefully.

Correct answer: B. Net charge enclosed by the surface is zero

Explanation: Step 1: In Gauss's law, net flux is directly related to net enclosed charge. Step 2: If net flux is zero, net enclosed charge is zero. Step 3: It is not necessary that electric field is zero at every point on the surface.

Correct answer: C. Irregular and asymmetric charge distribution

Explanation: Step 1: Gauss's law remains true in every case. Step 2: But finding electric field is simple only when symmetry exists. Step 3: In asymmetric distributions, separating field from total flux is difficult.

Correct answer: A. Because electric field inside the conductor is zero

Explanation: Step 1: In electrostatic equilibrium, electric field inside a conductor is zero. Step 2: Hence no net electric flux passes through a Gaussian surface inside. Step 3: By Gauss's law, net charge enclosed by it is also zero.

Correct answer: A. Because zero field inside means no excess enclosed charge can remain inside

Explanation: Step 1: Electric field inside a conductor is zero. Step 2: A small Gaussian surface inside gives zero flux and zero enclosed excess charge. Step 3: Therefore excess charge resides on the surface.

Correct answer: A. Because charge resides on the surface and field inside a conductor is zero

Explanation: Step 1: In a conductor, excess charge stays on the surface in electrostatic equilibrium. Step 2: Inside the conducting material, electric field remains zero. Step 3: Remember zero field inside a conducting sphere.

Correct answer: A. Because an inner Gaussian surface encloses no charge

Explanation: Step 1: Charge of a shell lies on its surface. Step 2: A spherical Gaussian surface inside the shell encloses no charge. Step 3: With symmetry and Gauss's law, field inside is zero.