Gauss's Law and its Applications

Step 1: Negative charge is induced on the inner surface to balance the positive cavity charge. Step 2: The conductor was initially neutral overall. Step 3: Therefore equal positive charge appears on the outer surface.

Step 1: A nearby outside charge can make field on the surface highly non-uniform. Step 2: Still, it is not enclosed by the closed surface. Step 3: Therefore its net contribution to total flux remains zero.

Step 1: Lines leaving indicate positive outward flux. Step 2: Lines entering contribute negative flux. Step 3: Since leaving is greater, net flux and enclosed charge are positive.

Step 1: Entering lines are negative for outward flux. Step 2: If their contribution is larger, total flux is negative. Step 3: Hence net enclosed charge is negative.

Step 1: Total flux is an overall surface sum of electric field. Step 2: To isolate field, its value or direction must be simple over the surface. Step 3: Symmetry provides this simplification.

Step 1: Both laws deal with electric field of stationary charges. Step 2: Applying Gauss's law to a point charge gives a result consistent with Coulomb's law. Step 3: Treat them as consistent, not contradictory.

Step 1: In Gauss's law, total flux is proportional to enclosed charge. Step 2: Since permittivity is unchanged, only charge change matters. Step 3: Tripling enclosed charge triples total flux.

Step 1: Total flux depends on net enclosed charge. Step 2: Rearranging charges may change field distribution on the surface. Step 3: But if net enclosed charge is same, total flux remains same.

Step 1: Gauss's law connects total flux through a closed surface to enclosed charge. Step 2: Changing area may alter local field values. Step 3: Still, if enclosed charge is same, total flux remains same.

Step 1: In Gauss's law, total flux is decided only by enclosed charge. Step 2: Outside charges may change field at the surface. Step 3: But they do not change total flux.

Step 1: In electrostatic equilibrium, field inside a conductor is zero. Step 2: This does not mean the conductor has no charge. Step 3: Excess charge can reside on its surface.

Step 1: Outside a spherical conductor, field behaves as if total charge is at the centre. Step 2: Like a point charge, it follows inverse-square dependence. Step 3: Doubling distance makes the field one-fourth.

Step 1: In electrostatic equilibrium, field at every interior point of a conductor is zero. Step 2: Changing radius of an internal Gaussian surface does not create enclosed net charge. Step 3: Therefore field remains zero.

Step 1: Gauss's law starts with enclosed charge. Step 2: Outside charges do not change total flux. Step 3: So first decide which charges are inside the surface.

Step 1: In Gauss's law, the surface completely encloses a volume. Step 2: Only for a closed surface is enclosed charge clearly defined. Step 3: Hence the law is not directly used in enclosed-charge form for an open surface.

Step 1: A point charge has spherical symmetry. Step 2: An infinite line has cylindrical symmetry. Step 3: An infinite sheet has plane symmetry, so a pillbox is useful.

Step 1: In Gauss's law, total flux is decided by enclosed charge. Step 2: Outside charges may create field on the surface but do not change total flux. Step 3: Always count the net charge inside the Gaussian surface.