What is the energy stored in the capacitor between terminals a and b of the network shown in the figure?

The circuit resembles a Wheatstone bridge with the capacitor between b and d as the bridge capacitor. Hence, it can be removed (replaced by an open circuit). By symmetry, the voltage on all other capacitors is the same. Let the voltage across all other capacitors be VC. Then, using KVL in loop 'abea', 2VC = 10. Therefore, VC = 5 V. The energy stored in each capacitor is given by E = (1/2)CV2. Therefore, E = 12.5 µJ.