The electric field at a point on equatorial of a dipole and direction of the dipole moment

Options

A. `180^(@)`
B. `0^(@)`
C. `45^(@)`
D. `90^(@)`

Answer

To solve the question regarding the electric field at a point on the equatorial line of a dipole and the direction of the dipole moment, we can follow these steps:

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

**Hint:** Remember that the dipole moment points from the negative charge to the positive charge.

### Step 2: Identify the Equatorial Point
The equatorial point of a dipole is located on the perpendicular bisector of the dipole. This means that if you draw a line through the center of the dipole at a right angle, any point along this line is considered an equatorial point.

**Hint:** The equatorial point is perpendicular to the line joining the two charges.

### Step 3: Analyze the Electric Field at the Equatorial Point
At the equatorial point, the electric fields due to both charges will have specific directions:
- The electric field due to the positive charge (+q) points away from the charge.
- The electric field due to the negative charge (-q) points towards the charge.

Since the equatorial point is equidistant from both charges, the magnitudes of the electric fields due to each charge will be equal, but their directions will be opposite.

**Hint:** The electric field due to the positive charge is directed away from it, while the electric field due to the negative charge is directed towards it.

### Step 4: Determine the Resultant Electric Field
At the equatorial point, the two electric fields will cancel each other out in the direction along the dipole axis, but they will add up in the perpendicular direction. Therefore, the resultant electric field at the equatorial point will be directed away from the dipole.

**Hint:** The resultant electric field at the equatorial point is the vector sum of the fields due to both charges.

### Step 5: Relate the Direction of the Electric Field to the Dipole Moment
The direction of the dipole moment is from the negative charge to the positive charge. Since the electric field at the equatorial point is directed away from the dipole, it is opposite to the direction of the dipole moment.

**Hint:** The dipole moment direction is opposite to the direction of the electric field at the equatorial point.

### Conclusion
Thus, the angle between the direction of the electric field at the equatorial point and the dipole moment is 180 degrees.

**Final Answer:** The electric field at a point on the equatorial of a dipole is directed opposite to the dipole moment, which corresponds to option A: 180 degrees.