A

To find the force pulling the dielectric inside the capacitor, we can follow these steps:
1. **Capacitance of the Capacitor with Dielectric**: The capacitance of a cylindrical capacitor with a dielectric of dielectric constant \( \epsilon \) filling the gap can be given by \( C = \frac{2 \pi \epsilon L}{ ext{ln}(\frac{b}{a})} \), where \( a \) is the inner radius and \( b \) is the outer radius of the cylindrical capacitor. Since the dielectric fills the width \( d \), we analyze the configuration.
2. **Electric Field (E)**: The electric field between the plates when connected to voltage \( U \) can be expressed as \( E = \frac{U}{d} \).
3. **Energy Stored (W)**: The energy stored in the capacitor can be calculated as \( W = \frac{1}{2} C U^2 \).
4. **Force Calculation**: The force acting on the dielectric due to the electric field can be derived from the change in energy with respect to the position of the dielectric being pulled into the capacitor. This is given by \( F = \frac{dW}{dx} \), where \( x \) is the position of the dielectric. For our case: \( F = \frac{1}{2} \epsilon E^2 \cdot A \), where \( A \) is the cross-sectional area of the capacitor.
Therefore, using these equations and substituting values, the resultant force can be explicitly formulated as a function of \( \epsilon, U, d, \text{ and } R \).
Thus, the pulling force of the dielectric is directly related to these variables and is given as: \( F = \frac{1}{2} \epsilon A E^2 = \frac{1}{2} \epsilon A \left(\frac{U}{d}\right)^2 \).
This expression indicates that the force depends on the parameters involved, and will be directed to pull the dielectric inside the capacitor.
Therefore, after thorough investigation of the physical principles, we identify the correct answer as option A.