Final answer:
The loss of energy after connecting the two charged spheres can be calculated using the charge difference and potential difference between the spheres. In this case, the loss of energy is 4.5 x 10^11 J.
Step-by-step explanation:
When two charged spheres are connected by a wire, their charges redistribute in order to reach equilibrium. In this case, the spheres have charges of 100 C and 50 C respectively. After they are connected, charge will flow from the sphere with higher charge to the one with lower charge until the charges are equal. The loss of energy after connection can be calculated using the equation:
Loss of energy = (Charge difference * Potential difference) / 2
Where the charge difference is the difference in charge between the two spheres and the potential difference is the difference in electric potential between the two spheres. In this case, the charge difference is 50 C and the potential difference can be calculated using the equation:
Potential difference = (k * q1 * q2) / r
Where k is the constant of electrostatics (approximately 9 x 10^9 N m^2/C^2), q1 and q2 are the charges on the spheres, and r is the distance between their centers (which is the sum of their radii in this case).
Substituting the values into the equations, we find:
Charge difference = 50 C
Potential difference = (9 x 10^9 N m^2/C^2) * (100 C) * (50 C) / (10 cm + 5 cm) = 1.8 x 10^10 V
Loss of energy = (50 C * 1.8 x 10^10 V) / 2 = 4.5 x 10^11 J