A dipole of dipole moment P is kept at the centre of a ring of radius R and charge Q. If the dipole lies along the axis of the ring. Electric force on the ring due to the dipole is : `(K = (1)/(4pi epsilon_(0)))`

Options

A. zero
B. `(KPQ)/(R^(3))`
C. `(2KPQ)/(R^(3))`
D. depends on the distribution of Q on the ring

Answer

To solve the problem of finding the electric force on a charged ring due to a dipole placed at its center, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a dipole with a dipole moment \( P \) located at the center of a ring of radius \( R \).
- The ring has a total charge \( Q \) uniformly distributed along its circumference.

2. **Electric Field Due to the Dipole**:
- The electric field \( E \) at a distance \( R \) from the dipole along its axis is given by the formula:
\[ E = \frac{k \cdot 2P}{R^3} \]
where \( k = \frac{1}{4\pi \epsilon_0} \).

3. **Force on the Ring**:
- The electric force \( F \) on the ring due to the dipole can be calculated using the formula:
\[ F = E \cdot Q \]
- Substituting the expression for \( E \):
\[ F = \left(\frac{k \cdot 2P}{R^3}\right) \cdot Q \]

4. **Final Expression for the Force**:
- Thus, the total electric force \( F \) on the ring due to the dipole is:
\[ F = \frac{2kPQ}{R^3} \]

### Final Answer:
The electric force on the ring due to the dipole is:
\[ F = \frac{2kPQ}{R^3} \]