Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.\ Assertion A: The electric field magnitude at an equatorial point at $3 \mathrm{~m}$ distance from the centre of a short dipole of dipole moment $9 	imes 10^{-6} \mathrm{C} \mathrm{m}$ is $3 	imes 10^3 \mathrm{~V/m}$.\ Reason R: The magnitude of the electric field on the equatorial line of a short dipole is $E = \frac{p}{4 \pi \varepsilon_0 r^3}$.\ In the light of the above statements, choose the correct answer.

Professor PC Thomas Classes · Answer

(a) : The electric field magnitude at an equatorial point of a short dipole is $E = \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^3}$. This makes Reason R true. Let's verify Assertion A by calculating $E$: $E = (9 	imes 10^9) 	imes \frac{9 	imes 10^{-6}}{3^3} = \frac{81 	imes 10^3}{27} = 3 	imes 10^3 \mathrm{~V/m}$. The assertion is also true, and the reason correctly explains it.