JEE Main 2019 — Physics solution

JEE Main2019Physics

A point dipole $p = p_{0} \overset{x}{^}$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively : (Take V = 0 at infinity)

A
$\frac{∣ p ∣}{4 π ε _{0} d ^{2}}, \frac{p}{4 π ε _{0} d ^{3}}$
B
$\frac{∣ p ∣}{4 π ε _{0} d ^{2}}, \frac{- p}{4 π ε _{0} d ^{3}}$
C
$0, \frac{- p}{4 π ε _{0} d ^{3}}$
D
$0, \frac{p}{4 π ε _{0} d ^{3}}$

Solution

$E = K \frac{p}{r ^{3}} 3 cos^{2} θ + 1 \Rightarrow θ = π /2 (0, d, 0) ∴ E = \frac{- k p}{d ^{3}}$

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