Question

The angle between the electric dipole moment of a dipole and the electric field strength due to it on the equatorial line is:

• A. \( 0^\circ \)
• B. \( 90^\circ \)
• C. \( 180^\circ \)
• D. \( 270^\circ \)

Hint:

For an electric dipole, the field at an axial point is along the dipole moment, while on the equatorial line, it is directed opposite to the dipole moment. Always use the dipole field formulas to determine directionality.

Answer 1

The Correct Option is C

In the context of electric dipoles, the equatorial line is the line perpendicular to the dipole's axis and passes through its midpoint. When dealing with the electric field due to a dipole, it is vital to understand the orientation and magnitude of the electric field on this equatorial line compared to the dipole moment.

The electric dipole moment (\( \mathbf{p} \)) is a vector quantity directed from the negative to the positive charge of the dipole. The electric field (\( \mathbf{E} \)) on the equatorial line of a dipole is directed opposite to the dipole moment.

The angle \(\theta\) between the electric dipole moment and the electric field strength \(\mathbf{E}\) on the equatorial line is \(180^\circ\), indicating that they are in opposite directions.

This can be conceptually understood because the electric field lines on the equatorial plane due to a dipole are directed such that they repel or leave the area near the positive charge and head towards the negative charge, effectively opposite to the direction of the dipole moment.

Thus, the correct answer is \(180^\circ\).

Answer 2

Step 1: Understanding the Concept of an Electric Dipole An electric dipole consists of two equal and opposite charges \( +q \) and \( -q \) separated by a distance \( 2a \). The electric dipole moment is given by: \[ \vec{p} = q \cdot 2a \] which points from the negative charge to the positive charge. 
Step 2: Electric Field on the Equatorial Line The equatorial line of a dipole is the perpendicular bisector of the dipole axis. The electric field at a point on the equatorial line due to the dipole is given by: \[ E_{\text{eq}} = \frac{1}{4\pi\varepsilon_0} \frac{p}{(r^2 + a^2)^{3/2}} \] This field is directed opposite to the dipole moment \( \vec{p} \), meaning it makes an angle of \( 180^\circ \) with the dipole moment. 
Step 3: Conclusion Since the electric field on the equatorial line is always directed opposite to the dipole moment, the angle between them is \( 180^\circ \).