Gauss's Law and its Applications

Step 1: Field lines emerge from positive charge. Step 2: Symmetry of an infinite sheet is same on both sides. Step 3: Hence field points away from the sheet on both sides.

Step 1: Field lines go toward negative charge. Step 2: Symmetry of an infinite sheet is same on both sides. Step 3: Therefore field points toward the sheet on both sides.

Step 1: Field lines emerge from a positive line charge. Step 2: Cylindrical symmetry makes the direction radial and perpendicular to the wire. Step 3: For positive wire, remember outward direction.

Step 1: Gauss's law gives correct total flux. Step 2: To find field, simple behaviour of field on the surface is needed. Step 3: In irregular distributions, this simplicity is absent.

Step 1: Net flux is proportional to enclosed net charge. Step 2: Surface area does not independently decide net flux. Step 3: Since enclosed charge is tripled, net flux becomes three times.

Step 1: Add the charges enclosed by the closed surface. Step 2: Positive two and negative five give a negative net charge. Step 3: Negative enclosed charge gives negative net flux.

Step 1: Outgoing lines give positive flux and incoming lines give negative flux. Step 2: If both are equal, net flux is zero. Step 3: Zero net flux means zero enclosed net charge.

Step 1: Net flux depends on enclosed net charge. Step 2: External charges can change field distribution on the surface. Step 3: If enclosed net charge remains same, net flux remains same.

Step 1: For a closed surface, outward normal is taken positive. Step 2: If field is opposite to it, the field is entering that part. Step 3: Therefore flux through that part is negative.

Step 1: Only the normal component crossing the surface contributes to flux. Step 2: Tangential component runs along the surface and does not pass through it. Step 3: Therefore flux is zero.

Step 1: Free charges in a conductor can move easily. Step 2: Any field component along the surface would keep them moving. Step 3: Hence in equilibrium, the outside field is normal to the surface.

Step 1: In both cases, an outside Gaussian surface encloses the whole charge. Step 2: Due to spherical symmetry, outside field is like a point charge. Step 3: The main difference lies in the field inside the sphere.

Step 1: In a conductor, excess charge stays on surface and inside field is zero. Step 2: In a solid non-conductor, charge is spread through volume. Step 3: Therefore field inside the non-conductor can increase outward from centre.

Step 1: Net flux is decided by enclosed net charge. Step 2: No charge is enclosed, so enclosed charge is zero. Step 3: External lines enter and leave equally, so net flux is zero.

Step 1: For a closed surface, outward direction is taken positive. Step 2: Positive net flux means outgoing contribution is greater. Step 3: It indicates positive net charge inside.

Step 1: For a closed surface, outward direction is positive. Step 2: Negative net flux means inward contribution is greater. Step 3: This indicates negative net charge inside.

Step 1: Field lines from an outside charge can cross the closed surface. Step 2: As many lines enter as leave. Step 3: Entry and exit cancel, giving zero net flux.

Step 1: Gaussian surface is a calculation tool, not necessarily a physical object. Step 2: If the new surface uses symmetry correctly, the result can remain same. Step 3: Do not spoil enclosed charge and field simplicity.

Step 1: For normal field, the full field component crosses the surface. Step 2: If magnitude is also simple, total flux is easy to find. Step 3: This is the aim of choosing a proper Gaussian surface.

Step 1: Flux comes from relation between electric field and area. Step 2: If electric field itself is zero, no field crosses the surface. Step 3: Therefore flux through that part is zero.

Step 1: A dipole has equal positive and negative charges. Step 2: If the whole dipole is inside, enclosed net charge is zero. Step 3: By Gauss's law, net flux is also zero.

Step 1: In Gauss's law, only charge inside the surface is counted. Step 2: Negative charge is inside and positive charge is outside. Step 3: Therefore enclosed net charge and net flux are negative.

Step 1: Net flux through a closed surface is decided by net enclosed charge. Step 2: Only positive charge is inside, so enclosed charge is positive. Step 3: Hence net flux is positive.

Step 1: Net flux is based on enclosed net charge. Step 2: Outside charges can change local field on the surface. Step 3: But they do not change net flux, so do not add them to enclosed charge.

Step 1: Gauss's law relates net flux to enclosed charge. Step 2: So first identify the closed surface and which charges are inside. Step 3: Then use symmetry to choose surface and calculate field.