Gauss's Law and its Applications

Step 1: For a closed surface, outward normal is taken positive. Step 2: If field is opposite to it, field lines are entering. 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: In electrostatic equilibrium, free charges in a conductor should not move. Step 2: A tangential field would make them move. Step 3: Therefore outside field at the surface remains normal.

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

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

Step 1: In Gauss's law, net flux is decided by enclosed net charge. Step 2: The enclosed charge is zero. Step 3: Lines from outside charges enter and leave equally, so net flux is zero.

Step 1: Outward direction is taken positive. Step 2: Positive net flux means outgoing contribution is greater. Step 3: This indicates positive net charge inside the closed surface.

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

Step 1: Field lines of an external charge can cross the closed surface. Step 2: Lines that enter also leave it. Step 3: Therefore entry and exit cancel and net flux is zero.

Step 1: Gaussian surface is a calculation tool. Step 2: If another surface also captures the symmetry correctly, the same physical field is obtained. Step 3: While changing surface, do not disturb enclosed charge and symmetry logic.

Step 1: For normal field, the full crossing component contributes. Step 2: If magnitude is also simple, total flux is easy to calculate. Step 3: This is why a proper Gaussian surface is chosen.

Step 1: Flux is related to electric field and area. Step 2: If field itself is zero, no electric effect crosses the surface. Step 3: Therefore flux through that part is zero.

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

Step 1: In Gauss's law, only the charge inside is counted. Step 2: The surface encloses negative charge while positive charge is outside. Step 3: Therefore net flux is negative.

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

Step 1: Enclosed net charge is the main factor for net flux. Step 2: Outside charges can change field on the surface but not total flux. Step 3: Do not add outside charges to enclosed charge.

Step 1: Gauss's law connects net flux with enclosed charge. Step 2: So first identify the closed surface and which charges are inside it. Step 3: Then use symmetry and calculate field if possible.

Step 1: Gauss's law relates total flux only to net enclosed charge. Step 2: When net charge is zero, positive and negative flux contributions may cancel. Step 3: Do not confuse zero total flux with zero field everywhere.

Step 1: Total flux depends on enclosed charge. Step 2: Changing radius still keeps the same point charge enclosed. Step 3: Therefore total flux does not change, although field on the surface changes.

Step 1: Field of a point charge varies inversely with square of distance. Step 2: Tripling radius makes square of distance nine times. Step 3: Hence field on the surface becomes one-ninth.

Step 1: Field due to a point charge decreases with distance. Step 2: At the same time, area of the sphere increases with square of distance. Step 3: These effects keep total flux fixed according to enclosed charge.

Step 1: In Gauss's law, only enclosed charge decides total flux. Step 2: The outside negative charge may create field on the surface, but its net flux contribution is zero. Step 3: Hence total outward flux remains positive.

Step 1: The sign of outward flux is linked to the sign of net enclosed charge. Step 2: Negative total flux means net field lines are inward. Step 3: Therefore net enclosed charge is negative.

Step 1: Total flux depends on net enclosed charge. Step 2: Three positive and two equal negative charges leave one positive charge as net. Step 3: Therefore total outward flux is positive.

Step 1: In Gauss's law, the sign of net enclosed charge gives the sign of total flux. Step 2: Two positive and five negative charges give net negative charge. Step 3: Hence total outward flux is negative.