What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line

Options

A. `0^(@)`
B. `90^(@)`
C. `180^(@)`
D. None of these

Explanation

To find the angle between the electric dipole moment and the electric field strength due to it on the equatorial line, we can follow these steps:

### Step 1: Understand the Electric Dipole
An electric dipole consists of two equal and opposite charges, +Q and -Q, separated by a distance 'd'. The dipole moment (p) is defined as:
\[ \vec{p} = Q \cdot \vec{d} \]
where the direction of the dipole moment is from the negative charge to the positive charge.

### Step 2: Identify the Equatorial Line
The equatorial line of an electric dipole is the line that is perpendicular to the dipole axis and lies in the plane that bisects the dipole. For a dipole aligned along the x-axis, the equatorial line would be along the y-axis.

### Step 3: Determine the Electric Field on the Equatorial Line
The electric field (E) due to a dipole at a point on the equatorial line is given by:
\[ E = \frac{1}{4\pi \epsilon_0} \cdot \frac{2p}{r^3} \]
where \( r \) is the distance from the center of the dipole to the point on the equatorial line.

### Step 4: Analyze the Directions of the Dipole Moment and Electric Field
- The dipole moment \(\vec{p}\) points from the negative charge (-Q) to the positive charge (+Q), which is along the x-axis.
- The electric field on the equatorial line is directed along the y-axis, perpendicular to the dipole moment.

### Step 5: Calculate the Angle
Since the dipole moment is along the x-axis and the electric field on the equatorial line is along the y-axis, the angle \(\theta\) between them can be calculated using the following:
- The angle between two perpendicular vectors is \(90^\circ\).

Thus, the angle between the electric dipole moment and the electric field strength due to it on the equatorial line is:
\[ \theta = 90^\circ \]

### Conclusion
The angle between the electric dipole moment and the electric field strength due to it on the equatorial line is \(90^\circ\).

---