Gauss's Law and its Applications

Step 1: Total flux depends on enclosed charge. Step 2: If the charge remains inside, the value of enclosed charge does not change. Step 3: Position change may change distribution of flux, not total flux.

Step 1: The charge is exactly at the centre. Step 2: All six faces of the cube are equally placed with respect to that charge. Step 3: Therefore total flux is equally divided among the six faces.

Step 1: A cube has six equal faces. Step 2: Since the charge is at the centre, symmetry gives equal flux through all faces. Step 3: Therefore one face gets one sixth of total flux.

Step 1: According to Gauss's law, sign of total flux is linked with sign of enclosed net charge. Step 2: Negative enclosed charge means field lines are net inward. Step 3: Therefore total flux is negative.

Step 1: For each small part of a closed surface, area vector is taken outward. Step 2: This makes outgoing flux positive and incoming flux negative. Step 3: This convention is very useful in sign-based questions.

Step 1: Inside a conductor at electrostatic equilibrium, electric field is zero. Step 2: A closed Gaussian surface inside has zero net flux. Step 3: By Gauss's law, excess charge enclosed by it is zero.

Step 1: Outward direction is taken positive for a closed surface. Step 2: Positive net flux means outgoing contribution is greater. Step 3: Thus outgoing lines are more than incoming lines.

Step 1: Field lines go toward negative charge. Step 2: For a long negative wire, symmetry makes field radial toward the wire. Step 3: Positive wire gives outward field and negative wire gives inward field.

Step 1: Field lines emerge from positive charge. Step 2: For an infinite sheet, field is normal to the sheet and outward on both sides. Step 3: Remember directions separately for positive and negative sheets.

Step 1: Field lines go toward negative charge. Step 2: On both sides of a negative infinite sheet, field points toward the sheet. Step 3: First check the sign of charge while deciding direction.

Step 1: First identify the symmetry of charge distribution. Step 2: Then choose a suitable Gaussian surface and find enclosed charge. Step 3: Finally relate total flux with electric field.

Step 1: Gauss's law connects total flux through a closed surface with net enclosed charge. Step 2: Shape or colour does not decide the total flux. Step 3: In such questions, identify enclosed charge first.

Step 1: Total flux is proportional to enclosed charge. Step 2: Doubling enclosed charge doubles the net source. Step 3: Therefore total flux also doubles.

Step 1: According to Gauss's law, total flux depends on enclosed charge. Step 2: Changing shape may alter field distribution on the surface. Step 3: But if enclosed charge remains the same, total flux is unchanged.

Step 1: The outside charge can create field on the surface. Step 2: Its lines both enter and leave the closed surface. Step 3: Since enclosed charge is zero, total flux is zero.

Step 1: Total flux depends on the sign of net enclosed charge. Step 2: Two positive and one equal negative charge give a positive net charge. Step 3: Hence total outward flux is positive.

Step 1: In Gauss's law, total flux through a closed surface is decided by net enclosed charge. Step 2: One positive and two equal negative charges give a negative net charge. Step 3: So total outward flux is negative.

Step 1: Gauss's law is true for every closed surface. Step 2: Calculation becomes easy when the chosen surface matches the symmetry. Step 3: Therefore identify symmetry first.

Step 1: The field from a point charge spreads symmetrically in all directions. Step 2: Every point on a centered sphere is at the same distance from the charge. Step 3: Therefore field magnitude is the same on the surface.

Step 1: Around an infinite line charge, the field is radial. Step 2: A coaxial cylinder matches this symmetry. Step 3: Therefore field magnitude can be treated as same on the curved part.

Step 1: For an infinite sheet, field is perpendicular to the surface. Step 2: Equal behavior on both sides makes the pillbox useful. Step 3: Remember this surface for plane symmetry.

Step 1: Charge of a spherical shell lies on its surface. Step 2: A Gaussian surface inside the shell encloses zero charge. Step 3: By symmetry, the field inside becomes zero.

Step 1: A spherical shell has spherical symmetry. Step 2: A Gaussian surface outside encloses the whole charge. Step 3: The outside field behaves like that of a point charge at the centre.

Step 1: Free charges in a conductor can move easily. Step 2: If an internal field exists, they keep moving. Step 3: Equilibrium is reached only when the internal field becomes zero.

Step 1: Inside a conductor in electrostatic equilibrium, electric field is zero. Step 2: For a Gaussian surface inside, total flux is zero. Step 3: So no excess net charge remains in the bulk; it resides on the surface.