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New Capacitance in Dielectric

Let Ua and ...

Question

Let $U_{a}$ and $U_{d}$ be the energy densities in air and in a dielectric of constant k for same field. Then,

U_{a} = U_{d}

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U_{a} = k U_{d}

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U_{d} = k U_{a}

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U_{a} = (k - 1) U_{d}

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Solution

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, $U_{d} = \frac{1}{2} (k ϵ_{0}) E^{2} = k \frac{1}{2} ϵ_{0} E^{2} = k U_{a}$

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