Gauss's Law and its Applications

Step 1: A spherical shell has spherical symmetry. Step 2: For an outside point, the Gaussian surface encloses the whole charge. Step 3: The result is like a point charge placed at the centre.

Step 1: Electric field of an infinite line charge is inversely proportional to distance. Step 2: When distance is doubled, the field becomes half. Step 3: For line charge, remember inverse relation with distance.

Step 1: Electric field of an infinite plane sheet does not depend on distance. Step 2: Even when distance is doubled, field remains the same. Step 3: Remember the difference between distance rules for plane sheet and point charge.

Step 1: An infinite plane sheet has symmetry along all directions in the plane. Step 2: Therefore field cannot prefer any direction along the sheet and must be normal to it. Step 3: Remember normal direction for plane sheet.

Step 1: Net flux through a closed surface depends on net enclosed charge. Step 2: Equal positive and negative charges add to zero. Step 3: Therefore net flux is zero, even though electric field may exist inside.

Step 1: In Gauss's law, only charge enclosed by the closed surface is counted. Step 2: The outside negative charge may change local field, but not net flux. Step 3: If positive charge is inside, net flux is determined by it.

Step 1: Net flux is a total over the whole closed surface. Step 2: To find electric field, the field must be separated in a simple way. Step 3: In asymmetry this is not possible, so direct field calculation is difficult.

Step 1: The purpose of a Gaussian surface is to simplify calculation. Step 2: It may be an imaginary closed surface and need not be a real object. Step 3: Choose it according to symmetry, not material.

Step 1: Outgoing field lines give positive flux. Step 2: If more lines leave than enter, net flux is positive. Step 3: Positive net flux means positive net charge inside.

Step 1: For a closed surface, outward direction is taken positive. Step 2: Entering lines give negative flux. Step 3: If more lines enter, net flux is negative and enclosed net charge is negative.

Step 1: Radius of the spherical surface is unchanged, so distance is unchanged. Step 2: Field of a point charge is proportional to source charge. Step 3: If charge doubles, field on the surface doubles.

Step 1: Total flux depends on net charge enclosed by the closed surface. Step 2: Changing radius does not change enclosed charge. Step 3: Therefore total flux remains same, though field value may change.

Step 1: Electric field of a point charge varies inversely as square of distance. Step 2: When radius doubles, square of distance becomes four times. Step 3: Hence field on the surface becomes one fourth.

Step 1: Total flux is decided only by enclosed charge, so it stays same. Step 2: On a larger sphere, the same flux spreads over larger area. Step 3: Therefore electric field per unit area decreases.

Step 1: Field from a positive line charge points outward. Step 2: On the curved surface of the cylinder, the field is radial and normal to the surface. Step 3: For a positive wire, remember radially outward direction.

Step 1: Field of a long wire is radial. Step 2: For the flat ends of the cylinder, the field lies parallel to those surfaces. Step 3: A field parallel to a surface gives zero flux through it.

Step 1: Field of an infinite plane sheet is perpendicular to the sheet. Step 2: For a pillbox Gaussian surface, this field is parallel to the curved side. Step 3: Therefore flux through the curved side is zero.

Step 1: Field just outside a conductor is related to surface charge density. Step 2: Higher surface charge density gives stronger electric field. Step 3: Remember stronger field near sharper regions.

Step 1: Free charges in a conductor can move easily. Step 2: If a field component existed along the surface, charges would keep moving. Step 3: Therefore, in electrostatic equilibrium, field is normal to the surface.

Step 1: An infinite uniformly charged sheet has strong symmetry. Step 2: This symmetry gives equal fields on both sides independent of distance. Step 3: For finite sheets, edge effects can disturb this simple result.

Step 1: Inside a uniformly charged solid non-conducting sphere, enclosed charge increases with radius. Step 2: As a result, field generally increases as we move outward from the centre. Step 3: Remember the difference between conductor and non-conducting solid sphere.

Step 1: At the centre of the sphere, symmetry exists in all directions. Step 2: Effects from opposite directions balance each other. Step 3: Therefore, electric field at the centre is zero.

Step 1: Outside the sphere, a Gaussian surface encloses the whole charge. Step 2: Due to spherical symmetry, outside field is like total charge at the centre. Step 3: From outside, a spherical charge distribution behaves like a point charge.

Step 1: For uniform and normal field, each small part contributes simply. Step 2: Total flux is electric field multiplied by total area. Step 3: This is the simplicity of symmetry-based Gauss calculation.

Step 1: Flux is related to field crossing a surface. Step 2: A field parallel to the surface does not pass through that part. Step 3: Therefore flux through that part is zero.