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Standard XII

Physics

Electric Field Due to a Dipole

A and B are...

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 distance from it. The field at $A$ and $B$ are ${\to E}_{A}$ and ${\to E}_{B}$ .

{\to E}_{A} = {\to E}_{B}

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{\to E}_{A} = 2 {\to E}_{B}

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{\to E}_{A} = - 2 {\to E}_{B}

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| E_{B} | = \frac{1}{2} | E_{A} |,

{\to E}_{B}

is perpendicular to

{\to E}_{A}

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Solution

The correct option is C ${\to E}_{A} = - 2 {\to E}_{B}$
For a point on the axis of a dipole,
$_{A} = \frac{2 \to p}{4 π ϵ_{0} {r_{A}}^{3}}$
For a point on the perpendicular bisector,
$_{A} = - \frac{\to p}{4 π ϵ_{0} {r_{B}}^{3}}$
Since, $r_{A} = r_{B}$
Hence, $_{A} = - 2_{B}$
Hence, C is the correct answer.

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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 distance from it. The field at A and B are →EA and →EB.

The correct option is C →EA=−2→EBFor a point on the axis of a dipole,→EA=2→p4πϵ0rA3For a point on the perpendicular bisector,→EA=−→p4πϵ0rB3Since, rA=rBHence, →EA=−2→EBHence, C is the correct answer.

$A$ 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 distance from it. The field at $A$ and $B$ are ${\to E}_{A}$ and ${\to E}_{B}$ .