Question

Assertion The electric field due to a dipole on its axis line at a distance $r$ is $E$. Then, electric field due to the same dipole on the equatorial line and at the same distance will be $E/2$.
Reason Electric field due to dipole varies inversely as the square of the distance.

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

Answer 1

Answer: (C)

We know that, for an electric dipole
$E_{\text{axial }}=\frac{1}{4\pi {\epsilon }_0}\left(\frac{2p}{r^3}\right)$ ...(i)
and $E_{\text{equatorial }}=\frac{1}{4\pi {\epsilon }_0}\left(\frac{p}{r^3}\right)$ ...(ii)
Hence, from Eqs. (i) and (ii), we get
$\frac{E_{\text{axil }}}{2}=E_{\text{equatorial }}$
Hence, $E_{\text{equatorial }}=E/2$
Reason is false as electric field due to dipole varies inversely as cube of distance,
i.e. $E\propto \frac{1}{r^3}$