capacitor problem hcv.

even i am getting same as your answer.

Energy stored per unit volume=1/2*εE²
E=kQ/r²=kQ/R*(R/r²)=VR/r²
Total energy=_R∫^2R1/2*ε*V²R²/r⁴*4Ï€r²dr=2πεV²R²_R∫^2R1/r²dr
=πεRV²

From another perspective:
The PE in charging the sphere to potential V is stored in the form of electric field.
V=kQ/R
PE=₀∫^Qkq/R*∂q=kQ²/2R=k*(VR/K)²/2R=V²R/2k=2πεV²R
Total energy stored in electric field=2πεV²R.
Hence in a concentric sphere of radius R energy must be less than the total.

Ans is πεRV².
The second explanation was just to prove that it connot be 2πεRV²,as it corresponds to total electrostatic energy.

Energy density is given by 12ε₀E² E=-Vr Energy density=12ε₀V²r² energy is = ∫_R^2R(12ε₀V²r²4Î r²)∂r = ∫(_R^2R2Πε₀V²)∂r=2Πε₀V²R