Gauss's Law and its Applications

The governing idea is that electric flux through a closed surface is the surface integral, Φ = ∮ E · dA. A closed surface may be divided conceptually into many small area elements, each having an area vector and a small flux contribution. Adding, or integrating, all these contributions gives the total flux. Therefore option A is correct; a point, straight line, or metal rod cannot represent the complete surface.

Electric flux is defined by Φ = ∮ E · dA. If the electric field has the same magnitude everywhere and is normal to the surface, the angle is zero, so E · dA = E dA. The integral therefore reduces to Φ = E∮dA = EA, where A is the total area. Thus option A is correct. It is not impossible or merely guessed, and it is not zero because the field crosses the surface normally.

A point charge produces a spherically symmetric electric field. On a spherical Gaussian surface centered on the charge, the field has no preferred tangential direction; it points along the radius. For a positive charge it is radially outward, and for a negative charge it is radially inward. Hence option A is correct. Circular, always horizontal, and always downward directions would depend on an external orientation and do not describe a point charge generally.

The electric field direction is defined by the force on a positive test charge. Since like charges repel, a positive source charge produces field lines directed away from itself. On a spherical Gaussian surface centered at that charge, the outward normal is radial, so the field is radially outward at every point. Therefore option A is correct. Inward direction belongs to a negative source charge, while parallel or circular directions do not follow spherical symmetry.

The electric field direction is the direction of force on a positive test charge. A negative source charge attracts such a test charge, so its field lines point toward the charge. On a spherical Gaussian surface centered on the negative charge, this means the field is radially inward, opposite to the outward area normal. Thus option A is correct; outward applies to a positive charge, while tangential or nonexistent field is incorrect.

Gauss's law states that the net electric flux through a closed surface equals the net charge enclosed by it divided by ε₀: Φ = Q_enclosed/ε₀. Therefore the algebraic sum of all charges located inside the chosen surface is called the enclosed charge, or net enclosed charge. Option A is correct. Charges outside the surface are not part of Q_enclosed, and heat, colour, and linear mass are unrelated physical quantities.

Gauss's law gives the net flux through a closed surface as Φ = Q_enclosed/ε₀. Here the enclosed charge is zero, even though charges may be present outside the surface. Therefore Φ = 0/ε₀ = 0. External charges can produce electric field through the surface and may give positive and negative local contributions, but those contributions cancel in the closed-surface total. Hence option A is correct, not positive, negative, or infinite.

Gauss's law connects the electric flux through a closed surface with the charge enclosed: Φ = Q_enclosed/ε₀. When the charge distribution has strong symmetry, a suitable Gaussian surface makes the field magnitude constant or gives a simple direction, allowing the electric field to be found efficiently. Common examples include spherical, cylindrical, and planar symmetry. Therefore option A is correct; the other choices are unrelated to this electrostatic law.

Electric flux is calculated from Φ = ∮ E · dA, where dA is the vector area element. For a closed surface, the conventional area vector at every point is directed along the outward normal. If the field has an outward component, the contribution is positive; an inward component gives a negative contribution. Thus option A is correct. North, downward, and tangential directions are not universal conventions for a closed surface.

The flux through a small surface element is dΦ = E · dA = EA cos θ, where θ is the angle between the electric field and the outward normal. If the field is parallel to the surface, it is perpendicular to the normal, so θ = 90° and cos 90° = 0. Therefore dΦ = 0 for that part. Option A is correct; maximum flux occurs when the field is normal to the surface, not parallel.

Gauss's law states that the net electric flux through a closed surface equals the enclosed charge divided by the permittivity of free space: Φ = Q_enclosed/ε₀. A closed boundary is essential because it lets us decide unambiguously which charges are enclosed and which are external. External charges may contribute locally to the field, but their net flux through the closed surface cancels. Thus option A is correct; the other options make false claims about area, field, or material.

Step 1: Gauss's law is applied to a closed surface. Step 2: It says total electric flux depends on the net charge enclosed inside. Step 3: In such questions, first check the enclosed charge.

Step 1: Gauss's law relates total flux to a closed surface. Step 2: A closed surface completely encloses a region. Step 3: Before using Gauss's law, check whether the surface is closed.

Step 1: A Gaussian surface need not be a real surface. Step 2: It is an imaginary closed surface chosen to simplify calculation. Step 3: Choose it according to symmetry.

Step 1: Gauss's law gives total flux through a closed surface. Step 2: This total flux depends on the net enclosed charge. Step 3: Changing shape does not change total flux if enclosed charge is unchanged.

Step 1: According to Gauss's law, total flux is linked to enclosed charge. Step 2: If net enclosed charge is zero, there is no net source. Step 3: Therefore total flux is zero.

Step 1: Field lines emerge outward from a positive charge. Step 2: Lines leaving the closed surface give positive outward flux. Step 3: Use the sign of charge to decide the sign of flux.

Step 1: Electric field lines go toward a negative charge. Step 2: With outward direction as reference, entering lines give negative flux. Step 3: Thus a negative enclosed charge gives negative outward flux.

Step 1: An outside charge can create electric field on the surface. Step 2: But its field lines enter and leave the closed surface. Step 3: So its net contribution to total flux is zero.

Step 1: Gauss's law is true for any closed surface. Step 2: But calculation becomes easy when there is spherical, cylindrical, or plane symmetry. Step 3: In applications, identify symmetry first.

Step 1: The field around a point charge spreads symmetrically in all directions. Step 2: This gives spherical symmetry. Step 3: A sphere centered at the charge is the simplest Gaussian surface.

Step 1: A long charged line has cylindrical symmetry. Step 2: The field is radial outward from the line. Step 3: Hence a coaxial cylinder is a convenient Gaussian surface.

Step 1: For a plane sheet, the field is perpendicular to the sheet. Step 2: A pillbox surface captures the equal field on both sides. Step 3: This is useful for plane symmetry.

Step 1: In electrostatic condition, free charges in a conductor rearrange. Step 2: The electric field inside a conductor becomes zero. Step 3: For conductor questions, note the electrostatic condition.

Step 1: Free charges can move in a conductor. Step 2: In electrostatic equilibrium, excess charge resides on the surface. Step 3: Do not assume excess charge remains inside the conductor.