Question

Let $U_a$ and $U_d$ be the energy densities in air and in a dielectric of constant k for same field. Then,

• A. $U_a=U_d$
• B. $U_a=k{U}_d$
• C. $U_d=k{U}_a$
• D. $U_a=(k-1)U_d$

Answer 1

The correct option is C $U_d=k{U}_a$

If $E$ is the electric field ,

energy density in air, $U_a=\frac{1}{2}{ϵ}_0{E}^2$ and

Energy density in dielectric, $U_d=\frac{1}{2}\left(k{ϵ}_0\right)E^2=k\frac{1}{2}{ϵ}_0{E}^2=k{U}_a$