Problem An insulating sphere carries a positive charge. Placed in vacuum 10 cm10\ \text{cm}10 cm from a point charge Q=−2 μCQ = -2\ \mu\text{C}Q=−2 μC, it experiences a force of magnitude 1,89 N1{,}89\ \text{N}1,89 N. Determine the charge on the sphere (treated as point-like). Solution Use k=8,99⋅109 N\cdotpm2/C2k = 8{,}99\cdot 10^9\ \text{N·m}^2/\text{C}^2k=8,99⋅109 N\cdotpm2/C2, r=10 cm=0,1 mr = 10\ \text{cm} = 0{,}1\ \text{m}r=10 cm=0,1 m, ∣Q∣=2 μC=2⋅10−6 C|Q| = 2\ \mu\text{C} = 2\cdot 10^{-6}\ \text{C}∣Q∣=2 μC=2⋅10−6 C. From Coulomb’s law F=k ∣Q∣ q/r2F = k\,|Q|\,q/r^2F=k∣Q∣q/r2, solve for charge qqq: q=F r2k ∣Q∣=1,89⋅(0,1)28,99⋅109⋅2⋅10−6=1,89⋅0,011,798⋅104=0,018917980≈1,05⋅10−6 Cq = \frac{F\,r^2}{k\,|Q|} = \frac{1{,}89\cdot (0{,}1)^2}{8{,}99\cdot 10^9\cdot 2\cdot 10^{-6}} = \frac{1{,}89\cdot 0{,}01}{1{,}798\cdot 10^4} = \frac{0{,}0189}{17980} \approx 1{,}05\cdot 10^{-6}\ \text{C}q=k∣Q∣Fr2=8,99⋅109⋅2⋅10−61,89⋅(0,1)2=1,798⋅1041,89⋅0,01=179800,0189≈1,05⋅10−6 C q≈1,05⋅10−6 C=1,05 μC\ev{q \approx 1{,}05\cdot 10^{-6}\ \text{C} = 1{,}05\ \mu\text{C}}q≈1,05⋅10−6 C=1,05 μC Links Topics: Elettrostatica Concepts: Legge di Coulomb Objects: Sfera carica