An ideal electric dipole of dipole moment p is placed at the origin, aligned along the positive x-axis. Two points, A and B, are located on the positive y-axis at distances d and 3d from the origin, respectively, as

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Correct answer: C. (E_0)/(27)

The electric field due to an ideal (short) dipole at a point on its equatorial axis is given by:

E = \dfrac{1}{4\pi\epsilon_0} \dfrac{p}{r^3}

Thus, the magnitude of the electric field is inversely proportional to the cube of the distance from the dipole,

E \propto \dfrac{1}{r^3}

.

For point A at distance

r = d

:

E_A = \dfrac{1}{4\pi\epsilon_0} \dfrac{p}{d^3} = E_0

For point B at distance

r = 3d

:

E_B = \dfrac{1}{4\pi\epsilon_0} \dfrac{p}{(3d)^3}

E_B = \dfrac{1}{27} \left( \dfrac{1}{4\pi\epsilon_0} \dfrac{p}{d^3} \right)

E_B = \dfrac{E_0}{27}

Answer:

\dfrac{E_0}{27}

An ideal electric dipole of dipole moment p is placed at the...

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