4. The capacitance of a capacitor is increased by a factor of 1.5 when it is completely filled with a certain dielectric material. Find the dielectric constant of the material and its
electric susceptibility

a. Dielectric constant, ε = 1.5 b. Electric susceptibility, χ = 0.5

Explanation:

a. Dielectric constant

Since the capacitance of the capacitor is increased by a factor of 1.5. Let its initial capacitance be C and its final capacitance after adding the material be C'.

Since C' = εC where ε = relative permittivity,

Also, C' = 1.5C

Comparing both equations for C', ε = 1.5.

Since ε = relative permittivity = dielectric constant,

dielectric constant = 1.5

So, the dielectric constant = 1.5

b. Electric susceptibility

The electric susceptibility χ is given by

χ = ε - 1 where ε = dielectric constant

Since ε = 1.5,

χ = ε - 1

χ = 1.5 - 1

χ = 0.5

So the electric susceptibility χ = 0.5

true tan speed = ang vel x radius