Question

The electric field intensity at a point on the equatorial line of a dipole and direction of the dipole moment
A. will be parallel
B. will be in opposite direction
C. will be perpendicular
D. are not related

Answer 1

Hint:Dipole is made of two charges positive and negative of the same magnitude. The equatorial line must be passed from the middle of the distance between the two opposite charges. A net electric field can be calculated on the equatorial line as the resultant of the two opposite charges which must be parallel to the distance between the charges.

Formula used
\[\overrightarrow {{E_{eq}}} = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{\overrightarrow p }}{{{r^3}}}\]
Where \[\overrightarrow p \] is dipole moment, \[{\varepsilon _0}\] is the permittivity of free space and r is the distance of the points from the center of the dipole.

Complete step by step solution:
As we know the electric field at a point on equatorial line is:
\[\overrightarrow {{E_{eq}}} = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{\overrightarrow p }}{{{r^3}}}\]
It will be directed from a positive charge to a negative charge. Here the electric field intensity at some point on the equatorial line will be perpendicular to the equatorial line.

The direction of the electric field at the equatorial point will be in the opposite direction as the direction of the dipole moment. At any point on the equatorial line of the dipole, the direction of the electric field(E) is parallel to the axis of the dipole which is opposite to the direction of dipole moment(p) and also is perpendicular to the equatorial line.

Hence option B is the correct answer.

Note: Electric dipole is defined as the combination of two equal and opposite charges separated by some distance. The direction of the electric dipole moment is from negative charge to positive charge.