First slide

Dipole

Question

A and B are two points on the axis and the perpendicular bisector, respectively, of an electric dipole. A and B are far away from the dipole and at equal distances from it. The fields at A and B are $\vec{E}$ _A and $\vec{E}$ _B Then

Moderate

A

${\vec{E}}_{A} = {\vec{E}}_{B}$
B

${\vec{E}}_{A} = 2 {\vec{E}}_{B}$
C

${\vec{E}}_{A} = - 2 {\vec{E}}_{B}$
D

$|{\vec{E}}_{B}| = \frac{1}{2} |{\vec{E}}_{A}|, and {\vec{E}}_{A} is perpendicular to {\vec{E}}_{B}$

Solution

Electric field due to dipole at axial position is
$E_{axial} = \frac{1}{4 π ε_{0}} \frac{2 p}{r^{3}} (along the dipole moment)$
Electric field due to dipole at equatorial position
$\begin{array}{l} E_{eq} = \frac{1}{4 π ε_{0}} \frac{p}{r^{3}} (opposite to dipole moment) \\ Hence {\vec{E}}_{A} = - 2 {\vec{E}}_{B} \end{array}$

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