a. When the electric field between the plates is 75% of the dielectric strength and energy density of the stored energy is 2800 J/m3, what is the value of the dielectric constant k?

Answer: The value of the dielectric constant k = 1.8

Explanation:

If C = ε A/d and

Electrostatic energy W = 1/2CV^2

Substitutes C in the first formula into the energy formula.

W = 1/2 ε A/d * V^2

Let us remember that electric field strength E is the ratio of potential V to the distance d. Where V = Ed

Substitute V = Ed into the energy W.

W = 1/2 * ε A/d * (Ed) ^2

W = 1/2 * ε A/d * E^2 * d^2

d will cancel one of the ds

W = 1/2 * ε Ad * E^2

W/Ad = 1/2 * ε * E^2

W/V = 1/2 * ε E^2

Where Ad = volume V

E = dielectric strength

εo = permittivity of free space = 8.84 x 10^-12 F/m

W/V = 2800 J/m^3

Let first calculate the dielectric strength

2800 = 1/2 * 8.84*10^-12 * E^2

5600 = 8.84*10^-12E^2

E^2 = 5600/8.84*10^-12

E = sqrt (6.3 * 10^14)

E = 25 * 10^7

75% of E = 18.9 * 10^6Jm

The permittivity of the material will be achieved by using the same formula

2800 = 1/2 * ε E^2

2800 = 0.5 * ε * (18.9*10^6) ^2

2800 = ε * 1.78 * 10^14

ε = 2800/1.78*10^14

ε = 1.57 * 10^-11

Dielectric constant k = relative permittivity

Relative permittivity is the ratio of the permittivity of the material to the permittivity of the vacuum in a free space. That is

k = 1.57*10^-11/8.84*10^-12

k = 1.776

k = 1.8 approximately

Therefore, the value of the dielectric constant k is 1.8