# Energy stored

**Electricity and Magnetism**Level 5

The distance between their centers is \(X\) and \( X << R\)

Find the total electrostatic energy stored in the system 3.

If it is given by the expression \( \dfrac {a {\rho}^{b} R^c X^d \pi } {e \epsilon } \) for positive integers \(a,b,c,d,e\) with \(a,e\) coprime, what is the value of \(a+b+c+d+e\)?

Hint: Energy density in electric field is given by \( \dfrac { \epsilon E^2}{2} \).

**Details and Assumptions**:

\( \rho \) stands for charge per unit volume.

\(X\) is the distance between the centers in configuration 3.

\(R\) is the radius of each cloud .