A

Step 1: The energy stored outside the uniformly charged sphere is given as U₀ joules.
Step 2: The formula for the self-energy of a uniformly charged sphere can be expressed as:
Self-energy (U) = \frac{3Q^2}{5R}
Step 3: The electric field due to a uniformly charged sphere of radius R (for points outside the sphere) is equivalent to that of a point charge Q located at the center of the sphere. Therefore, the potential outside the sphere is given by V = \frac{Q}{4\pi \epsilon_0 r}, where r is the distance from the center.
Step 4: The potential energy of a charge Q at this potential V is U = Q \cdot V = Q \cdot \frac{Q}{4 \pi \epsilon_0 r}.
Step 5: To find the total self-energy, we consider that the sphere is built up slowly from infinitesimal charges. The total self-energy U can be derived to be:
U = \frac{3Q^2}{5R}.
Step 6: Since we need to express U in terms of U₀, we recognize that U₀ is a different energy level representation related to the sphere's charge configuration.
Conclusion: For a uniformly charged sphere, the self-energy can be shown to be equal to 5U₀/3, where the energy stored outside contributes to this energy fraction. Hence, we write:
U = \frac{5}{3} U₀
Therefore, the self energy of the sphere in terms of U₀ is: \frac{3}{5} U₀.