Question

6. Calculate the polarization produced in dielectric medium of dielectric constant 6 when it is subjected to an electric field of 100 Vm–1. (e0 = 8.854 × 10–12 Fm–1)

Answer 1

The polarization produced in a dielectric medium with a dielectric constant of 6 and subjected to an electric field of 100 Vm–1 is 4.427 × 10–10 C²/N·m².

Step-by-step explanation:

The question asks us to calculate the polarization produced in a dielectric medium of dielectric constant 6 when it is subjected to an electric field of 100 Vm–1. The polarization P in a material is related to the electric field E and the electric constant (ε₀) through the equation P = (ε_r - 1)ε₀E, where ε_r is the dielectric constant of the material. Given that ε₀ = 8.854 × 10–12 Fm–1, ε_r = 6, and E = 100 Vm–1, we can calculate the polarization as follows:

P = (6 - 1) × 8.854 × 10–12 Fm–1 × 100 Vm–1

P = 5 × 8.854 × 10–12 C²/N·m² × 100 Vm–1

P = 4.427 × 10–10 C²/N·m²

The polarization P in the dielectric medium is 4.427 × 10–10 C²/N·m².

Answer 2

The polarization produced in the dielectric medium with a dielectric constant of 6 when subjected to an electric field of 100 V/m is 4.427 × 10⁻¹⁰ C/m².

Step-by-step explanation:

To calculate the polarization (P) produced in a dielectric medium when subjected to an electric field (E), we can use the relationship between polarization, the electric field, and the electric susceptibility (χe) of the dielectric medium. The electric susceptibility is related to the dielectric constant (k) by the equation χe = k - 1. The polarization is then given by P = ε0χeE where ε0 is the permittivity of free space. Given the dielectric constant k = 6 and an electric field E = 100 V/m, and using ε0 = 8.854 × 10−12 F/m (farads per meter), we calculate the polarization.

Step 1: Calculate the electric susceptibility:
χe = k - 1 = 6 - 1 = 5.

Step 2: Calculate the polarization:

P = ε0χeE = 8.854 × 10−12 F/m × 5 × 100 V/m = 4.427 × 10−10 C/m2.

Therefore, the polarization produced in the dielectric medium is 4.427 × 10−10 C/m2.