# Energy stored in a capacitor with dielectric

This is a problem from a book. The exact words of the problem are below:

A condenser of 1 µF contains titanium oxide ($$\TiO_2\$$) as a dielecric with $$\ε_r\$$ = 100. For an applied D-C voltage of 1000 volts, find the energy stored in the condenser as well as the energy stored in polarizing the titanium oxide. Answer the same questions for a 1 µF mica condenser, assuming a dielectric constant of $$\ε_r\$$ = 5.4 for mica.

For $$\TiO_2\$$ dielectric, 0.5 and 0.495 joules; for mica dielectric, 0.5 and .407 joules.

I could calculate the energy stored in the capacitor as 0.5J but I didn't know how to calculate the energy stored in polarizing a dielectric as above. There seem no reference materials to know how to do it. What is the correct method to calculate the energy stored in polarizing the dielectric? Capacitor and condenser means the same thing.

Reference:

Electrical engineering materials, A.J.Dekker, PHI, 2014, page 59.

If the dielectric was not there, the capacitance would the same as if $$\ε_r\$$ =1.