Question 15: Electrostats & Capacitance

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.

Accepted Answer

We know that, for an electric dipole
$$\begin{aligned}
E_{	ext {axial }} & =\frac{1}{4 \pi \varepsilon_0}\left(\frac{2 p}{r^3}ight) \quad 	ext{..... (i)}\
	ext{and} \quad E_{	ext {equatorial }} & =\frac{1}{4 \pi \varepsilon_0}\left(\frac{p}{r^3}ight) \quad 	ext{.... (ii)}
\end{aligned}$$
Hence, from Eqs. (i) and (ii), we get
$$\frac{E_{	ext {axil }}}{2}=E_{	ext {equatorial }}$$
Hence, $$\quad E_{	ext {equatorial }}=E / 2$$
Reason is false as electric field due to dipole varies inversely as cube of distance, i.e.
$$E \propto \frac{1}{r^3}$$

Answer

Both assertion and reason are true and reason is the correct explanation of assertion

Answer

Both assertion and reason are true but reason is not the correct explanation of assertion

Answer

Assertion is true but reason is false

Answer

Both assertion and reason are false.

Electrostats & Capacitance

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.

Choose the correct answer: