A uniform spherical volume charge distribution of radius 2 m, centered at the origin, has a strength of . A point charge of strength  is moved from (  ) to (  ) in Cartesian coordinate system. The relative permittivity of the medium is 1 and the coordinate values are in meters.

The work done during the process is  

(Round off to two decimal places)

Let . The value of , where V is the volume enclosed by the unit cube defined by 0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 1, and 0 ≤ 𝑧 ≤ 1, is

The static electric field inside a dielectric medium with relative permittivity, , expressed in cylindrical coordinate system is given by the following expression

where , ,  are unit vectors along r,  and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, , in SI units is given by:

Let ,  and  be unit vectors along r,  and z directions, respectively in the cylindrical coordinate system. For the electric flux density given by  , the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:

The figures show diagrammatic representations of vector fields  . Respectively. Which one of the following choices is true?        

A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R (> r) is

The direction of vector A is radially outward from the oigin, with  where  and k is a constant. The value of n for which  is

Two point charges  and  are placed at coordinates (1, 1, 0) and (−1, −1, 0) respectively.  The total electric flux passing through a plane z = 20 will be

Given a vector field, the divergence theorem states that

In an electrostatic field . ( True=1, False=0)

Which of the following equations represents the Gauss’ law in a homogeneous isotropic medium?