Question

Assertion : In the absence of an externally applied electric field, the displacement per unit volume of a polar dielectric material is always zero.
Reason : In polar dielectrics, each molecule has a permanent dipole moment but these are randomly oriented in the absence of an externally applied electric field.

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (A)

The displacement vector is given by
$\vec{D}={\epsilon }_0\vec{E}+\vec{P}$ where
$\vec{E}=$ applied electric field and
$\vec{P}=$ polarisation or dipole moment per unit volume
$=n\vec{p}\times 2[\vec{p}$ is the component of dipole moment of each molecule in direction $\vec{E}$ and $n$ is the no. of molecules per unit volume]
Now in the absence of an electric field $(\vec{E}=0)$ the polarisation vector $\vec{p}$ vanishes (because $\vec{p}$ is there if $\vec{E}$ is there).
Therefore displacement $\vec{D}=0$