Test: Gauss Law - JEE MCQ

A point charge is single dimensional. The three dimensional imaginary enclosed surface of a point charge will be sphere.

This is because when a charge is given to a hollow sphere that is a spherical shell then all charges will reside on its surface and as we know that electric field is directly proportional to given charge . so according to this concept of gauss’s law we can say about this point.

Given that, A charge q is placed at the centre of open end Q a cylindrical vessel,we have to find the flux through the surface of the vessel.
so, when charge Q is placed at the centre of open end of a cylindrical vessel then only half of the charge will contribute to the flux, because half will lie inside the surface and half will lie outside the surface.
so, flux through the surface of vessel is q/2ε0

Electric flux is a scalar quantity. It is a scalar because it is the dot product of two vector quantities, electric field and the perpendicular differential area.

An isolated conductor is any metal object not connected to or not in contact with any other conductor . one of its common properties is that there is no charge of any nature within the surface of the conductor. All charge, if any, always resides on the outer surface only.thus , if we place any amount of charge, it would tend to reside on its surface.

we know that the flux linked with a Gaussian surface is given as
Φ = E.ds = q/ε₀
here,
q = 8.85x10^-8 C
ε0 = 8.85x10^-12 F/m
so,
Φ = 8.85x10^-8 / 8.85x10^-12 
thus, flux will be
Φ = 10⁴ Nm²/C^-1

As surface of area lies in the Y-Z plane, thus its area vector points in X direction i.e.   A=10i
Electric flux    ϕ=E.A
∴   ϕ=(6i+3j​+4k).(10i)
⟹   ϕ=6×10=60 unit

If the radius of the spherical shell is double then also flux associated with spherical surface remain unchanged because the charge enclosed in system always remains unchanged.

A line charge can be visualized as a rod of electric charges. The three dimensional imaginary enclosed surface of a rod can be a cylinder.

In case of a sphere (solid/hollow), electric intensity (E) at an external point varies as 1/r2, where r is the distance of the point from the centre of the sphere. In case of a line charge, E o 1/r and in case of an infinite plane sheet of charge, E does not depend upon r.