Gauss's Law and its Applications

Step 1: Sign of total flux is linked with sign of net enclosed charge. Step 2: Negative total flux indicates negative net enclosed charge. Step 3: Look at the sign of total flux, not just local field direction.

Step 1: In Gauss's law, total flux is proportional to net enclosed charge. Step 2: Positive flux means net enclosed charge is positive. Step 3: Do not be confused by field direction at only one part of the surface.

Step 1: Take algebraic sum of enclosed charges. Step 2: Two positive charges and one equal negative charge leave a positive net charge. Step 3: Therefore total flux is positive.

Step 1: Take algebraic sum of charges inside the closed surface. Step 2: Two equal positive and two equal negative charges give zero net charge. Step 3: Hence total flux is zero.

Step 1: Gauss's law is generally true. Step 2: To find field easily, symmetry is needed so that field becomes simple. Step 3: Without symmetry, the law is valid but calculation becomes difficult.

Step 1: Total flux is determined by net enclosed charge. Step 2: The charge is inside the surface, whether at centre or not. Step 3: Thus total flux is same, though field distribution is not uniform.

Step 1: In Gauss's law, only enclosed charge is counted. Step 2: The charge has moved outside, so enclosed net charge is zero. Step 3: Therefore total closed flux is zero.

Step 1: If field is zero on the surface, flux through every part is zero. Step 2: By Gauss's law, zero total flux means net enclosed charge is zero. Step 3: Individual charges may exist inside, but net charge is zero.

Step 1: Total flux is the algebraic sum over the whole closed surface. Step 2: Different parts may give positive and negative contributions. Step 3: Zero total flux does not mean field is zero everywhere.

Step 1: A long line charge has cylindrical symmetry. Step 2: No special direction exists along the line, so field is radial. Step 3: For positive line it is outward and for negative line inward.

Step 1: Field lines emerge from positive charge. Step 2: Symmetry of an infinite plane sheet makes field perpendicular to the sheet. Step 3: Therefore on both sides the field is away from the sheet.

Step 1: Field lines terminate on negative charge. Step 2: For an infinite sheet, field is perpendicular to the plane. Step 3: Hence on both sides, the field points toward the negative sheet.

Step 1: If net charge were enclosed, Gauss's law would give non-zero flux. Step 2: Non-zero flux requires electric field on the surface. Step 3: Since field inside an electrostatic conductor is zero, net charge cannot be inside.

Step 1: Gauss's law connects total flux with a closed surface. Step 2: For an open surface, inside and outside are not clearly defined. Step 3: Therefore Gaussian surface must be closed.

Step 1: Field of a positive point charge is radially outward. Step 2: Area vector of a spherical surface is also radially outward. Step 3: Both are in the same direction, so the angle is zero degree.

Step 1: Field due to a negative charge points toward the centre. Step 2: The area vector of the closed spherical surface points outward. Step 3: They are opposite, so the angle is 180 degrees.

Step 1: Gauss's law is valid for any closed surface. Step 2: If field is not uniform, calculating total flux is not simple. Step 3: So the law is valid, but application may be difficult.

Step 1: For flux, field must cross the surface. Step 2: Field parallel to a surface does not cross it. Step 3: Therefore every contribution is zero and total flux is zero.

Step 1: In electrostatic condition, electric field inside conductor material is zero. Step 2: Zero field gives zero total flux through the closed surface. Step 3: Therefore net charge enclosed by that Gaussian surface is zero.

Step 1: Leaving field lines indicate positive flux. Step 2: More outgoing lines show positive total flux. Step 3: By Gauss's law, net enclosed charge is positive.

Step 1: Entering field lines indicate negative flux. Step 2: More entry gives negative total flux. Step 3: Therefore net enclosed charge is negative.

Step 1: Entry gives negative flux and exit gives positive flux. Step 2: If both are equal, total flux is zero. Step 3: By Gauss's law, net enclosed charge is zero.

Step 1: Total flux is algebraic sum over the whole closed surface. Step 2: Some parts may have local negative flux. Step 3: If positive contribution is greater, total flux remains positive.

Step 1: External charges can produce electric field on the surface. Step 2: Their field lines both enter and leave the closed surface. Step 3: Thus total flux can be zero while local field is non-zero.

Step 1: Charge on a conductor resides on its surface. Step 2: Near sharp parts, charge can be more concentrated. Step 3: Higher surface charge density gives stronger electric field nearby.