Gauss's Law and its Applications

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.