The electric flux density of a surface with permittivity of 2 is given by 12 units. What the flux density of the surface in air?

To find the electric flux density ((D)) in air given the electric flux density of a surface with permittivity ((ε)) of 2, we should understand the relation given by the equation:

[ D = εE ]

where:

– (D) is the electric flux density,

– (ε) is the permittivity of the material, and

– (E) is the electric field intensity.

Given:

[ D = 12 , text{units} ]

[ ε = 2 ]

First, we find the electric field intensity ((E)) using the given information. In the given medium (permittivity = 2),

[ 12 = 2 times E ]

[ E = frac{12}{2} = 6 , text{units} ]

Now, to find the flux density in air, we use the permittivity of free space ((ε_0)), which is approximately (1) in normalized units for this context (since we’re considering relative permittivity and the original question implies a normalized context by not specifying units). If exact values and SI units are required, (ε_0 = 8.854 times 10^{-12} , text{F/m}) in vacuum or air, but we’ll stick to the normalized unit context here for direct comparison.

Thus, for air (with (ε_{text{air