The loss in potential energy of the two spheres after the connection is determined as -5.4 x 10¹³ J.
Energy of the spheres before the connection
The potential energy of the spheres before the connections is calculated as follows;
V1 = (kq)/r
V1 = (9 x 10⁹ x 100)/(0.05)
V1 = 1.8 x 10¹³ J
V₂ = (9 x 10⁹ x 50)/(0.01)
V₂ = 4.5 x 10¹³ J
Total energy = (4.5 + 1.8) x 10 10¹³ J = 6.3 x 10¹³ J
- Total charge of spheres after connection = q₁ + q₂ = 100 c + 50 c = 150 c
- Radius of the spheres after connection = 15 cm
V = (9 x 10⁹ x 150)/(0.15)
V = 9 x 10¹²J
Loss in energy
ΔV = 9 x 10¹²J - 6.3 x 10¹³ J
ΔV = -5.4 x 10¹³ J
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