Two electric dipoles are placed in such a manner that their electric dipole moments are directed towards each other. The force between them will be

Options

A. attractive
B. inversely proportional to the cube of distance between charges
C. nversely proportional to the fourth power of the distance between charges
D. zero

Explanation

To solve the problem of determining the force between two electric dipoles that are directed towards each other, we can follow these steps:

### Step 1: Understand the Configuration of the Dipoles
Two electric dipoles are given, and their dipole moments (denoted as \( \mathbf{P_1} \) and \( \mathbf{P_2} \)) are directed towards each other. This means that if one dipole has a moment pointing in one direction, the other dipole's moment points in the opposite direction.

**Hint:** Visualize the dipoles as arrows pointing towards each other.

### Step 2: Determine the Nature of the Force
When two dipoles are oriented such that their dipole moments are directed towards each other, they will experience an attractive force. This is because opposite dipole moments attract each other, while like dipole moments repel each other.

**Hint:** Recall that opposite charges attract and like charges repel.

### Step 3: Use the Formula for the Force Between Dipoles
The force \( F \) between two electric dipoles can be expressed as:
\[ F = \frac{3}{2 \pi \epsilon_0} \frac{P_1 P_2}{r^4} \]
where:
- \( P_1 \) and \( P_2 \) are the magnitudes of the dipole moments,
- \( r \) is the distance between the dipoles,
- \( \epsilon_0 \) is the permittivity of free space.

**Hint:** Remember that the force depends on the product of the dipole moments and inversely on the fourth power of the distance.

### Step 4: Analyze the Relationship of the Force with Distance
From the formula, we can see that the force is inversely proportional to \( r^4 \). This means as the distance \( r \) increases, the force decreases rapidly.

**Hint:** Think about how the force changes as you move the dipoles further apart.

### Step 5: Conclusion
Since the dipoles are directed towards each other, the force between them is attractive. Therefore, the final answer is that the force between the two dipoles is attractive and follows the relationship given by the formula.

**Final Answer:** The force between the two electric dipoles is attractive.