Gauss's Law and its Applications

Step 1: In an electrostatic conductor, free charges on the surface are at rest. Step 2: A tangential component of an oblique field would move them. Step 3: Therefore the field outside must be perpendicular to the surface.

Step 1: Inside conductor material in electrostatic condition, electric field is zero. Step 2: Therefore total flux through an internal closed surface is zero. Step 3: By Gauss's law, net charge enclosed by that surface must be zero.

Step 1: Electric field inside an electrostatic conductor must be zero. Step 2: If excess net charge were inside, Gauss's law would give non-zero flux. Step 3: Hence excess charge arranges itself on the surface.

Step 1: Electric field inside conductor material is zero. Step 2: An empty cavity has no internal charge to start or end field lines. Step 3: In electrostatic condition, the conductor shields the cavity, so field inside it is zero.

Step 1: Even with a charge in the cavity, conductor material maintains zero field in electrostatic condition. Step 2: Induced charges on surfaces arrange to ensure this. Step 3: Therefore electric field inside conductor material remains zero.

Step 1: Electric field inside conductor material must be zero. Step 2: A Gaussian surface in conductor material around the cavity has zero flux. Step 3: Hence induced charge on the inner surface must be equal and opposite to the positive charge in the cavity.

Step 1: Field just outside a conductor surface depends on surface charge density. Step 2: Denser charge gives denser field lines. Step 3: Therefore field can be stronger near sharp parts.

Step 1: Outward field gives positive flux through a closed surface. Step 2: Non-zero outward field everywhere gives positive total flux. Step 3: By Gauss's law, net enclosed charge is positive.

Step 1: Area vector of a closed surface is outward. Step 2: Inward field is opposite to the area vector. Step 3: Total flux is negative, so net enclosed charge is negative.

Step 1: If net enclosed charge is zero, total flux must be zero. Step 2: If field is outward everywhere, every part gives positive contribution. Step 3: That gives positive total flux, so the statement is inconsistent.

Step 1: Gauss's law relates total flux to a closed surface. Step 2: For an open surface, inside and outside are not clearly defined. Step 3: Therefore the Gaussian surface must be closed.

Step 1: Flux comes from the component of field crossing the surface. Step 2: A parallel field does not pass through the surface. Step 3: Hence flux through every part and total flux are zero.

Step 1: In 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: Hence positive flux and zero enclosed charge are inconsistent.

Step 1: Gauss's law remains true even without symmetry. Step 2: But to find field, flux must be written in a simple form. Step 3: Without symmetry, field is not uniform or simply directed on the surface.

Step 1: External charge can change field direction and magnitude on the surface. Step 2: But in Gauss's law total flux is determined by net enclosed charge. Step 3: If enclosed charge is positive, total flux remains positive.

Step 1: Outside a conducting sphere, field behaves like that of a point charge at the centre. Step 2: Point charge field decreases inversely as square of distance. Step 3: Doubling distance makes field one fourth.

Step 1: Field of a long line charge is inversely proportional to distance. Step 2: Doubling distance halves the field. Step 3: Do not confuse it with inverse square relation of point charge.

Step 1: For an infinite plane sheet, Gauss's law gives field independent of distance. Step 2: Doubling distance does not change the field in the ideal infinite sheet case. Step 3: This result depends on infinite sheet symmetry.

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

Step 1: In this special case, total flux equals field times total area. Step 2: Field is unchanged and area is doubled. Step 3: Therefore total flux doubles, meaning enclosed charge must also be doubled.

Step 1: Area vectors of a closed surface point outward. Step 2: Inward field is opposite to them. Step 3: Hence total flux is negative and net enclosed charge is negative.

Step 1: Inside a conductor in electrostatic condition, electric field is zero. Step 2: A small pillbox can be chosen crossing the surface. Step 3: This gives a simple relation between flux through the outer face and surface charge density.

Step 1: Total flux is an algebraic sum. Step 2: Contributions from different parts may cancel even when local field is non-zero. Step 3: Therefore zero total flux does not mean field is zero everywhere.

Step 1: Gauss's law gives total flux. Step 2: Total flux is a surface sum, not field at one point. Step 3: Strong symmetry is needed to extract the electric field simply.

Step 1: Gauss's law for total flux requires a closed surface. Step 2: Total flux is determined by net enclosed charge. Step 3: To find field, symmetry is needed, so check these three things first.