Gauss's Law and its Applications

Step 1: Inside a conductor in electrostatic equilibrium, electric field is zero. Step 2: So total flux through a Gaussian surface inside it is zero. Step 3: Hence net enclosed charge is zero.

Step 1: A spherical conductor has spherical symmetry. Step 2: For outside points, its field behaves as if the whole charge were concentrated at the centre. Step 3: Treat it like a point charge for outside field.

Step 1: Take a Gaussian surface inside the spherical shell with no charge enclosed. Step 2: Since enclosed charge is zero, total flux is zero. Step 3: By symmetry, the electric field inside is zero.

Step 1: An infinite plane sheet has plane symmetry. Step 2: From Gauss's law, the field does not depend on distance. Step 3: Remember this for the ideal infinite sheet model.

Step 1: A long charged line has cylindrical symmetry. Step 2: The field is perpendicular to the line in radial direction. Step 3: For positive line charge it is outward and for negative line charge inward.

Step 1: For an infinite line charge, a cylindrical Gaussian surface is used. Step 2: From Gauss's law, the field varies inversely with distance. Step 3: Remember line charge and point charge have different distance dependence.

Step 1: In electrostatic equilibrium, tangential field cannot exist on a conductor surface. Step 2: If it existed, charges would move along the surface. Step 3: Hence the field is perpendicular to the surface.

Step 1: Gauss's law relates charge and electric field in electrostatics. Step 2: It is consistent with Coulomb's law and can be understood from it. Step 3: Do not confuse it with current or heat laws.

Step 1: Electric flux is related to electric field and area. Step 2: Electric field has unit newton per coulomb and area has metre squared. Step 3: So flux has unit newton metre squared per coulomb.

Step 1: In Gauss's law, total flux is proportional to enclosed charge. Step 2: Doubling the charge doubles the net source. Step 3: Therefore total flux doubles.

Step 1: A Gaussian surface is chosen to simplify calculation. Step 2: A good surface matches the symmetry of charge distribution. Step 3: Identify spherical, cylindrical, and plane symmetry separately.

Step 1: By Gauss's law, total flux through a closed surface depends on enclosed charge. Step 2: Changing area or shape may change local field. Step 3: But if enclosed charge is same, total flux remains same.

Step 1: Total flux depends on net enclosed charge. Step 2: Two equal positive and two equal negative charges make net charge zero. Step 3: Therefore total flux is zero.

Step 1: A point charge has spherical symmetry. Step 2: Applying Gauss's law gives the same distance dependence as Coulomb's law. Step 3: Thus both are connected in electrostatics.

Step 1: A plane sheet has plane symmetry. Step 2: The field is perpendicular to the sheet. Step 3: For a positive sheet it points away, and for a negative sheet it points toward the sheet.

Step 1: Field lines emerge outward from positive charge. Step 2: An infinite sheet has the same symmetry on both sides. Step 3: Therefore the field points away from the sheet on both sides.

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

Step 1: A line charge has cylindrical symmetry. Step 2: Gauss's law gives field inversely proportional to distance. Step 3: Remember it separately from inverse-square point charge field.

Step 1: A point charge has spherical symmetry. Step 2: Gauss's law gives its field inversely proportional to square of distance. Step 3: Compare this with line charge and sheet results.

Step 1: An infinite sheet looks symmetric at every point. Step 2: In Gauss's law calculation, distance dependence does not remain. Step 3: This result applies to the ideal infinite sheet.

Step 1: Total flux is linked to enclosed charge. Step 2: If total flux is zero, net enclosed charge is zero. Step 3: This does not mean field is zero everywhere on the surface.

Step 1: Gauss's law relates charge and electric field. Step 2: It is especially useful for finding fields of symmetric distributions. Step 3: For non-symmetric cases, the law is true but calculation may be difficult.

Step 1: In Gauss's law, total flux is decided only by enclosed charge. Step 2: An outside positive charge may create field on the surface. Step 3: But with no enclosed charge, total flux is zero.

Step 1: A Gaussian surface is chosen for calculation. Step 2: It need not be a real object. Step 3: It is commonly imagined according to symmetry.

Step 1: In spherical symmetry, all directions are related to the centre equally. Step 2: Therefore field is radial outward or inward. Step 3: For positive charge it is outward and for negative inward.