Gauss's Law and its Applications

Step 1: Field of an infinite plane sheet does not depend on distance. Step 2: Changing distance does not change its symmetry result. Step 3: Therefore electric field remains same.

Step 1: Field of an infinite sheet is normal to the sheet. Step 2: In the pillbox, this field runs along the curved surface. Step 3: Hence no flux passes through the curved part.

Step 1: Equal opposite charges have zero net charge. Step 2: But they are at different positions, so their fields do not cancel everywhere. Step 3: Zero net flux and zero local field are different ideas.

Step 1: Inside a conductor in electrostatic equilibrium, electric field is zero. Step 2: Therefore net flux through an internal closed Gaussian surface is zero. Step 3: By Gauss's law, enclosed excess charge is zero.

Step 1: Free charges in a conductor can move. Step 2: If a field component exists along the surface, charges will not remain at rest. Step 3: Hence in equilibrium, field is normal to the surface.

Step 1: A conductor in electrostatic equilibrium can shield an empty cavity from external influence. Step 2: Free charges rearrange so that field inside the cavity becomes zero. Step 3: Remember this as electrostatic shielding.

Step 1: In conducting material at electrostatic equilibrium, electric field must be zero. Step 2: The charge in the cavity induces charges on surfaces. Step 3: Still the net field inside the conducting material remains zero.

Step 1: Charge of a uniformly charged shell lies on its surface. Step 2: A Gaussian surface chosen inside the shell encloses no charge. Step 3: Hence total flux is zero and field is zero.

Step 1: An outside spherical Gaussian surface encloses the whole charge. Step 2: Spherical symmetry makes field same at equal distance. Step 3: The result is like total charge placed at the centre.

Step 1: Inside such a solid sphere, electric field is proportional to distance from centre. Step 2: Halving distance reduces the enclosed-charge effect accordingly. Step 3: Therefore field becomes half.

Step 1: At the centre, all directions are equivalent. Step 2: Electric effect from one direction balances that from the opposite direction. Step 3: Hence resultant electric field at the centre is zero.

Step 1: Outside the sphere, field behaves like total charge at the centre. Step 2: Field of a point charge varies inversely as square of distance. Step 3: Doubling distance makes field one fourth.

Step 1: Only the component crossing the surface contributes to flux. Step 2: If field is not normal everywhere, angle can vary. Step 3: Use simple multiplication only when field is uniform and normal.

Step 1: Net flux is decided only by enclosed net charge. Step 2: External positive charges may change local field but not net flux. Step 3: With negative net charge inside, flux remains negative.

Step 1: Initially the surface enclosed positive net charge, so flux was positive. Step 2: Including an equal negative charge makes net enclosed charge zero. Step 3: Zero enclosed net charge gives zero net flux.

Step 1: A spherical Gaussian surface centered on the point charge is chosen. Step 2: Every point of that surface is at the same distance from the charge. Step 3: Therefore field magnitude is same everywhere on it.

Step 1: Field of an infinite sheet has equal magnitude on both sides. Step 2: The pillbox has two flat faces on the two sides. Step 3: Thus both equal face contributions are added to get total flux.

Step 1: Positive charge acts as a source of field lines. Step 2: Symmetry of an infinite sheet is same on both sides. Step 3: Therefore field points away from the sheet on both sides.

Step 1: Negative charge is treated as a sink of field lines. Step 2: Symmetry of an infinite sheet is same on both sides. Step 3: Hence field points toward the sheet on both sides.

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

Step 1: Gauss's law correctly gives total flux. Step 2: To find electric field, simple field behaviour on the surface is needed. Step 3: Without symmetry, this simplicity is absent.

Step 1: Net flux depends on net enclosed charge. Step 2: Surface area alone does not decide total flux. Step 3: Since enclosed charge is tripled, net flux becomes three times.

Step 1: Add the charges inside the closed surface. Step 2: Positive two and negative five give a negative net result. Step 3: Therefore by Gauss's law, total flux is negative.

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: By Gauss's law, net enclosed charge is zero.

Step 1: Net flux is decided by net enclosed charge. Step 2: Outside charges can change field distribution on the surface. Step 3: Still net flux remains same if enclosed net charge is unchanged.