Gauss's Law and its Applications

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.